David Cameron will not commit funds to help bail Greece out because "it is not for Britain to bail our Eurozone countries".
However, he told Parliament, "if Greece were to leave the euro and wanted humanitarian assistance, I am sure that this house and the British public would take a more generous view".
"Sorting out the problems of the eurozone, which we've always warned about, is a matter for eurozone countries."
The prime minister also said that the IMF view that Greece needs debt relief "must be right".
David Cameron believes a solution can be found to provide bridge financing to Greece while not putting British taxpayers' money on the line, a spokeswoman said.
"We have always been clear that British taxpayers' money is not going to be used to provide finance for a euro zone Greek deal and that therefore this is a non-starter," Cameron's spokeswoman said.
"From the discussions that have been taking place this morning, it's clear that a number of other countries have concerns about this. I think there are a number of solutions that can be found."
Spanish Prime Minister Mariano Rajoy says he will put the details of a third Greek bailout to his own parliament for debate and ask for its approval.
Rajoy's People's Party holds an absolute majority in parliament. He did not say when the vote would take place.
"Even though this step is not obligatory in our country, it is my intent to take it to parliament for debate and possible approval (...) because there are a lot of funds that Spanish taxpayers are being asked to guarantee," Rajoy told parliament.
Most eurozone governments will wait until the proposals have been through the Greek parliament before raising the issue at home.
Greece's Energy Minister has denounced the latest EU bailout deal and called on the Prime Minister to refuse to implement it.
Panagiotis Lafazanis said Alexis Tsipras should cancel the legislation before it reached parliament, saying it was forced on Athens by lead eurozone lender Germany and its allies, who had acted like "financial assassins".
"The deal is unacceptable," he said. "It may pass through parliament but the people will never accept it and will be united in their fight against it."
Alexis Tsipras faces a difficult day in Parliament as he tries to persuade his party to back a Euro bailout he doesn't 'believe' in.Read the full story ›
Huge debt relief is needed for Greece if its economy is to recover and the country become self-supporting, a senior International Monetary Fund official has said.
The IMF updated its projections on Monday of Greece's financing needs and concluded that the country's debt situation was "unsustainable," said the official, who spoke on condition of anonymity.
That means the country's European creditors need to either write down the debt they are owed, or give Greece a grace period of as long as 30 years.
We have made it clear ... we need a concrete and ambitious solution to the debt problem. I don't think this is a gimmick or kicking the can down the road ... If you were to give them 30 years grace you are allowing them in the meantime to bring down debt by ... getting some growth back
Alexis Tsipras has said that the bailout deal he agreed with Eurozone leaders is one he does not believe in but is willing to implement it and take responsibility for it.
Speaking on Greek television, the country's prime minister also said he believed that last week's referendum would not put the country's euro membership at risk, but that Greece's lenders have displayed a vindictive stance.
The Greek finance ministry has submitted legislation, required by a deal struck with its international lenders, to parliament.
Prime Minister Alexis Tsipras has until Wednesday night to pass the measures, which include VAT and pension reforms, in order to start negotiations with European creditors on a third bailout.
Greek Prime Minister Alexis Tsipras faces a showdown with rebels in his own party and coalition partners as he battles to win support for the third bailout offered by the eurozone leaders.
The terms imposed by international lenders led by Germany in all-night talks at an emergency summit obliged Tsipras to abandon promises of ending austerity.
Instead he must pass legislation to cut pensions, increase VAT, clamp down on collective bargaining agreements and put much of the country's economy in the hands of its creditors.
If the deal falls through, Greece's banks face collapse and the country could finally be forced to leave the euro.
The latest bailout is conditional on Greece passing all the agreed reforms - including raising tax revenue and liberalising the labour market - in parliament by Wednesday.
Finance ministers from all 28 EU countries are holding a scheduled meeting in Brussels later this morning, where they will discuss the situation in Greece.
The Chancellor is seeking to block any move by the EU to use hundreds of millions of pounds of UK taxpayer's money in the latest efforts to rescue the Greek economy from oblivion.
In a series of telephone conversations with counterparts ahead of a meeting in Brussels later today, George Osborne is said to have made clear that ignoring a 2010 agreement by using the EU budget as collateral against short-term loans for Athens was a "non-starter".
A Treasury source said: "Our eurozone colleagues have received the message loud and clear that it would not be acceptable for this issue of British support for eurozone bailouts to be revisited.
"The idea that British taxpayers' money is going to be on the line in this latest Greek deal is a non-starter."