Standard and Poor's has downgraded Greece's credit rating to B-, just one notch above the range indicating vulnerability to a default.
It warned Athens had limited time to reach a deal with creditors.
"In our view, a prolongation of talks with official creditors could also lead to further pressure on financial stability in the form of deposit withdrawals and, in a worst-case scenario, the imposition of capital controls and a loss of access to lender-of-last-resort financing, potentially resulting in Greece's exclusion" from the eurozone, the ratings agency said in a statement.
Moody's has also placed Greece's credit rating on review for a downgrade, citing "high uncertainty" about the country's talks with creditors.
Moody's currently holds a deep junk-level rating of Caa1 on Greece's government bonds.
The agency said, "There is considerable uncertainty regarding the outcome of the ensuing negotiations, and the ability of the two sides to reach an agreement which secures Greece's financing position."
"If the Greek government is unable to secure an agreement with official creditors in the next few weeks, the probability of default on debt issued to the private sector would rise sharply."
Eurogroup to hold extraordinary meeting over Greek bailout
Euro zone finance ministers will hold an extraordinary meeting in Brussels to discuss the stand-off over Greece's bailout next Wednesday, Dutch Finance Minister Jeroen Dijsselbloem said.
The meeting will be the first chance for Greek Finance Minister Yaris Varoufakis to set out to sceptical colleagues the new government's demands for a reduction in Greece's debt and an end to austerity.
"Extra Eurogroup on Greece on Wednesday 11 Feb," Dijsselbloem, who heads the Eurogroup of finance ministers from the 19 countries that use the euro, said on Twitter.
Leaders of the 28 European Union nations, including new Greek Prime Minister Alexis Tsipras, will meet in Brussels the following day for a summit that is officially meant to focus on terrorism and Ukraine but will likely have to tackle Greece.
Mr Dijsselbloem had a notably chilly encounter with Mr Varoufakis - the "rock star" former economics professor who has caused a stir with his casual dress and radical plans - in Athens on 31 January.
Sources had already told AFP on Tuesday that a Eurogroup meeting on 11 January was very likely and would give Mr Varoufakis a chance to "put his ideas on the table".
Mr Tsipras and Mr Varoufakis, whose radical left Syriza party stormed to victory in elections on 25 January, have gone on a tour of major European capitals in recent days to build support for a renegotiation of the country's €240bn EU-IMF bailout.