Their meeting was the first in a round of scheduled meetings between Clinton and Greece's leadership during her visit to Athens, where she arrived late on Saturday from neighbouring Turkey after attending a meeting of the Contact Group for Libya.
Clinton underlined that the government of Greek Prime Minister George Papandreou had faced tough decisions and expressed Washington's support for his determination to carry out reforms.
Doing nothing would have far worse consequences than the current difficulties, she added, expressing her faith in the resilience of the Greek people.
"I applaud the Greek government on its willingness to take these difficult steps. Greece has inspired the world before, and I have every confidence that you are doing so again," she said.
She stressed that the Greek government was on the right path and that the reforms it had carried out were like "chemotherapy" and would make the country more competitive and more attractive to investors.
"I am not here to in any way downplay the immediate challenges because they are real. But I am here to say that we believe strongly that this will give Greece a very strong economy going forward," Clinton said.
Lambrinidis stressed that the Greece of today bore no relation to the Greece of the past and he emphasised the need for European solidarity in order to overcome the crisis. He also underlined the government's determination to forge ahead with reforms.
"We believe that we shall come out of this difficulty victorious," he said. "Many on both sides of the Atlantic have bet on the collapse of Greece and then have been proven wrong. We will continue to prove them wrong."
During one-on-one talks lasting half an hour, followed by a meeting between Greek and U.S. delegations, Clinton and Lambrinidis discussed the economic crisis and issues of foreign policy, focusing mainly on the situation in Libya, the Middle East, the western Balkans, the Cyprus issue and Greece's relations with Turkey.
Concerning the Cyprus issue, Lambrinidis expressed his conviction that progress was possible and had to be striven for, while noting that the necessary political will on Turkey's part was an essential precondition for success.
Referring to the crisis in Libya, Clinton thanked the Greek government for its willingness to receive NATO force at the naval base in Souda and Athens' support after the attack on the U.S. Embassy in Damascus. She said the two sides had shared views concerning the process of democratisation in north Africa and welcomed Athens' stance on the EU accession of the western Balkan countries.
After her meeting with Lambrinidis, the U.S. Secretary of State attended a working dinner with the prime minister at his offices.
Arriving for the dinner, she conveyed her family's warm regards to Papandreou and, on a lighter note in response to questions posed by a U.S. journalist, expressed her excitement that the U.S. women's soccer team will be playing in the World Cup final against Japan on Sunday night.
She said that U.S. Vice-President Joe Biden and her own daughter Chelsea would be in Frankfurt to watch the game and support the U.S. team, while she would be watching the game from Athens.
Sources in the government said her talks with the premier covered the economic crisis, foreign policy issues, the problems faced by the Ecumenical Patriarchate in Istanbul, energy issues and the 'Arab Spring', as well as Greece's role in the surrounding region.
There was complete agreement during the meeting on the need for a comprehensive and effective solution for the crisis in both Greece and in Europe, in order to send markets a clear message and deal effectively with speculators.
There followed a meeting between Clinton and Greek President Karolos Papoulias. A meeting between Clinton and Greece's main opposition New Democracy party leader Antonis Samaras is to take place on Monday.
Τhe Communist Party (KKE), in an announcement, claimed that the "US Secretary of State rewarded the (Greek) government's barbarous policy and supported the country's greater involvement in America's and its allies' imperialistic plans and wars against the countries of Africa and Mideast. This alliance is useful for Greek plutocracy and, therefore, is supported by ruling PASOK and main opposition New Democracy and other parties."
On its part, the Popular Orthodox Party (LA.O.S) party said the "US is showing Europe that it is ready to bring back the 'lost sheep'. The worst is that the Greek government is reacting as a 'lost sheep', and a black one, no less".
Finally, the Radical Left Coalition (SYRIZA) expressed its apprehension and its opposition to the Clinton visit. "The aim of her visit is not to assist in Greek people's problems and the issue of peace, but to ensure Greece's greater involvement in US, NATO and Israeli war plans against Afghanistan, Libya and in the wider region."
Meeting with FinMin
Government vice-president and Finance Minister Evangelos Venizelos underlined the importance of US support in Greece's effort to face the ongoing economic crisis, speaking during his meeting on Sunday with US Secretary of State Hillary Clinton.
"The US role is decisive in the IMF, and also the US's contacts with eurozone countries are also very important," Venizelos said, adding that Washington is taking under consideration Athens' every small positive step towards combating tax evasion and the collection of state revenues, as well as towards the implementation of a privatisation programme.
Moreover, Venizelos stressed that the "economic problem in Greece is political."
Greece, US sign bilateral agreement on protection of antiquities
In a visit to the new Acropolis Museum on Sunday, U.S. Secretary of State Hillary Clinton put her signature to a bilateral Greek-US agreement placing restrictions on the movement of archaeological and Byzantine artifacts dating up to the 15th century AD.
The agreement was signed in the Museum gallery with a view of the Parthenon and Athens Acropolis, with Greek Foreign Minister Stavros Lambrinidis and in the presence of Greece's Culture and Tourism Minister Pavlos Geroulanos.
Signing the agreement she conveyed the U.S. government's warm support both for Greece's future and the protection of its past. Looking up at the Acropolis, she noted that a nation that had built the Parthenon and invented democracy was able to face any difficulty.
In a brief address welcoming the U.S. Secretary of State to the museum, Lambrinidis said that Greece suffered from the illegal excavation and trade in antiquities and cultural artifacts that the agreement signed on Sunday was designed to fight.
Clinton underlined that the bilateral agreement will provide protection of Greece's heritage from theft and antiquities-smuggling, since the import of artifacts in to the United States will be illegal unless they are accompanied by a certificate issued by Greek authorities permitting them to leave the country.
She noted that this was the 15th agreement of this type signed by the U.S. with other countries, from Cambodia to Cyprus, and had been proved particularly effective. She also underlined that the U.S. had a 40-year-long tradition of devotion to preserving world heritage.