Mr Tsipras said he had failed to reach agreement with mainstream parties because of his insistence on rejecting austerity measures demanded by the EU and IMF as part of a bailout deal.
He made the announcement after talks with the Pasok and New Democracy parties, which support the bailout.
Pasok leader Evangelos Venizelos is now expected to try to form a coalition.
But if he in turn fails, Greece could face fresh elections within weeks.
An earlier attempt by New Democracy (ND) leader Antonis Samaras to form a coalition failed on Monday.
…a new tranche of bailout funds scheduled to go to Greece tomorrow will be delivered as planned, according to reports out of the European Financial Stability Facility meeting.
However it is unclear whether the full €5.2bn will be disbursed; the EFSF is discussing a smaller payout as a way of sending a signal to Greece that the bailout is not unconditional.
And, from earlier in the day
New York University economics professor and renowned prophet of economic end times Nouriel Roubini, aka Dr. Doom, says Europe is suffering a “slow motion train wreck” – and the boxcars could be piling up for years.
“Europe will be lucky if it ends up in stagnation like Japan for the next ten years,” Roubini told CNBC. Earlier in the day, Roubini said that Spain could exit the eurozone in three years from now.
No reports on whether he said so through a barely suppressed smile.
Or if he was stroking a white cat at the time…
Update From today’s, Thursday’s, Guardian Eurozone crisis live-blog
After yesterday’s toing-and-froing, the European Financial Stability Fund has confirmed this morning that it has sent €4.2bn to Greece today. €1bn has thus been held back, while Europe assesses the sitution/puts pressure on Athens.
Klaus Regling, head of the EFSF, said this €1bn would not be dispatched until the IMF, EU, ECB Troika has conducted a visit to Greece, assessed the situation, and agreed Greece’s financial program for the second half of 2012.