In an interview with the Financial Times, Mr Yatseniuk complained bitterly of constant attacks from a governing coalition that includes 136 MPs from the president's party, saying it was "uncomfortable [to be] stabbed in the back", Censor.NET informs.
Parliament, he noted, had failed to pass 60 per cent of government bills. But Mr Yatseniuk defended his record, insisting Ukraine was an "entirely different country" from 2014, when a revolution ousted pro-Russian president Viktor Yanukovych.
His comments came amid intense backroom political manoeuvring, with the US-born finance minister Natalie Jaresko and the parliament speaker Volodymyr Hroisman said by political insiders to have been sounded out over the premier's job.
"If the president doesn't want to work with me, and if his faction strongly oppose this government and this prime minister... I kindly request with all due respect to take the responsibility to form the government, to present the programme of the new government to the Ukrainian people, and to form a new coalition," Mr Yatseniuk said.
"Take it or leave it, back me or sack me."
Ukraine's deepest political crisis since the 2014 revolution was triggered by last month's resignation of the economy minister Aivaras Abromavicius, who said it had become impossible to implement reforms.
Mr Yatseniuk's government survived a no-confidence motion in parliament. But he admitted his government had been weakened after some coalition MPs supported the vote and two of its five constituent parties withdrew.
Political uncertainty risks derailing international financial support for Ukraine amid continued attempts by Russia to destabilise it and pull it back into Moscow's sphere of influence.
The IMF has delayed disbursement of the next tranche of a $17.5bn aid package until it is clear the government can continue pushing through structural reforms. One senior official warned Ukraine's financial reserves would last only six to eight months without IMF support.
Some political commentators draw parallels with the rift between president Viktor Yushchenko and premier Yulia Tymoshenko that ultimately undermined Ukraine's 2004 pro-democracy "Orange" revolution.
Mr Yatseniuk said he had "always tried to avoid the notorious 2005 scenario". "I will never complain about my president... I will bite my lip to the end. But the end is too far," he quipped.
The prime minister did not dispute reports that Ms Jaresko and others had been in talks over the top job, but declined to comment further.
"My government survived a confidence vote," he said. "I am absolutely open for any type of discussion. But... any government needs to get the support of the house," he said.
People familiar with the situation told the FT this week that representatives of Mr Poroshenko and Mr Yatseniuk's parliamentary factions had offered to back Ms Jaresko in the premier's job, but talks stalled.
One political insider suggested the premier might initially have supported such a scenario as a way out of the crisis, but later concluded the finance minister lacked parliamentary backing to be an effective long-term premier.
Mr Yatseniuk said the country faced three scenarios - a reshuffled government headed by him, a new government or snap elections. He was "ready with all honour to hand over the office of the prime minister to the strongest government, the strongest coalition, and the best programme".
Some of his former political allies appeared to favour early polls, he added, but this was misguided.
"After any snap parliamentary elections, trust me, they will never be able to form any pro-reformist and pro-western government," he added, saying any new coalition would comprise "10 different parties with entirely different ideologies".
The premier insisted that corruption allegations levelled against him and associates by opponents were "groundless". "This is slander and defamation," he said.
Mr Yatseniuk said he had "to beg, to plead, to attack the house" to get parliament to back legislation. He had presented one privatisation bill 15 times.
But he added, "this country is entirely different than it was two years ago... new police, new army, new fiscal policy, new energy policy, new social policy, new folks sitting in the government... very strong society".
"I have done everything I can, in these current circumstances. I can do more, but we need to press down on the accelerator."
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