* Varoufakis says Athens willing to consider tax commission
* In blog, Varoufakis says can discuss pensions, retirement
* Ministers see no deal in Riga, want progress speeded up
By Robin Emmott and Jan Strupczewski
RIGA, April 24 (Reuters) - Greece offered some concessions on Friday on reforms demanded by international lenders in return for new funding before Athens runs out of money, but euro zone creditors said negotiations needed to speed up to get a deal by June.
After talks with German Chancellor Angela Merkel on Thursday in Brussels, Greek Prime Minister Alexis Tsipras said he wanted a deal by the end of this month. Merkel, in a comment seen as underlining the determination of Europe's main paymaster to keep Greece in the euro zone, said "everything must be undertaken to prevent" Athens running out of cash.
In a blog published as euro zone finance ministers met in Riga to assess progress on a reform-for-cash package to ward off a Greek default, Finance Minister Yanis Varoufakis agreed to some of the lenders' conditions, still declaring that the euro zone must drop "an approach that has failed".
"The current disagreements with our partners are not unbridgeable," Varoufakis wrote in the blog, saying that he was open to some privatisations and an independent tax commission. He rejected any more wage or pension cuts and said he wanted leeway on the government's primary budget surplus targets.
"Our government is eager to rationalize the pension system (for example, by limiting early retirement), proceed with partial privatisation of public assets, ... create a fully independent tax commission," Varoufakis said.
Those reform pledges could ease tensions following three months of largely fruitless talks since radical leftists won power in Athens on a promise to reverse austerity and renegotiate Greece's 240-billion euro bailout package.
European Commission Vice President Valdis Dombrovskis said there would not be a deal in the Latvian capital and told Greece to accelerate its work on a reform list.
Slovak Finance Minister Peter Kazimir, who confessed to being "just a bit tired" of the Greek saga, said the end of June was now the final date for a deal because Greece's bailout expires then.
Already investors are looking to the next finance ministers' meeting in Brussels on May 11, but several euro zone officials told Reuters they do not expect a deal then either. Greece is due to pay 750 million euros back to the International Monetary Fund the following day.
"There is a great sense of urgency for all of us. I have spoken to my colleagues in Athens and they're very determined to get the deal. They know that the time is running out," said Jeroen Dijsselbloem, chairman of the Eurogroup of ministers.