But his true motives for plunging the country into fresh political chaos, and picking a perilous fight with parliament, have more to do with pique, personal rivalry and the erratic whims of an autocratic and unwell president.
Ministers who steal MrYeltsin's thunder rarely last long, at least during the periods in which he is fit enough to turn up for work. Yevgeny Primakov, his third prime minister in just over a year, was no exception.
Tensions surfaced soon after Mr Primakov, the former foreign minister, took office last year and tried to cobble together a political truce between the Kremlin and a hostile, Communist-dominated lower house of parliament, the Duma. Mr Yeltsin was asked to forgo some powers, including suspending his right to sack the government. Typically, he balked.
Catapulted into office as the president's second-choice premier after last August's financial meltdown (the Duma rejected the first candidate, Viktor Chernomyrdin), Mr Primakov arrived amid predictions of civil unrest and economic collapse.
It did not happen. Instead, he established a measure of stability in which the rouble - though a quarter of its 1997 value against the dollar - was holding its own. The economy was stagnant, but tiny glimmers of hope had just begun to appear. Oil prices, a crucial source of Russian revenues, were at last rallying. A tentative $4.5bn (pounds 2.8bn) deal was last month put together with the International Monetary Fund (IMF), albeit one that stood a strong chance of collapsing.
The Russian stock market this week reached its highest point in a year.
Russia's long-suffering 146-million population was impressed and relieved. Mr Primakov's experience and apparatchik's manner reassured many among the impoverished millions who blame corrupted pro-Western reformers for Russia's demise.
He became the most trusted politician in the country. Although old (he is 69), unhealthy and - he insists - unwilling, he was soon seen as favourite for the presidency. Polls invariably placed him as the second round winner of an election.
Mr Yeltsin evidently hated it. While he was sidelined by illness, Mr Primakov's stature and authority grew, enhanced by his coalition-building skills based on strong ties with parliament. Back at work, Mr Yeltsin sought to reassert his power, and began publicly to humiliate his premier. Kremlin staff made no secret that Mr Primakov was dispensable; whispers ran around Moscow that he would soon be axed.
Another murkier issue may also be entangled with this affair. Mr Primakov had sworn to clean up corruption. During his term, investigators began to pursue the business magnate Boris Berezovsky, an adviser of the first family and a friend of the president's younger daughter, Tatyana Dyachenko.
They set their sights on several firms with which the mogul has links, including the giant airline Aeroflot, run by the President's son-in-law.
The Kremlin was uneasy. Members of its inner circle found themselves in the cross-hairs as prosecutors probed claims that some of the President's senior staff farmed out lucrative building contracts in return for kickbacks. The investigations, still incomplete, formally come under the auspices of the hapless prosecutor-general, Yuri Skuratov, whom the Kremlin tried in vain to persuade parliament to oust by brandishing a secretly recorded video showing him having sex with prostitutes. But the moving force was thought to come from within the Primakov administration and its parliamentary allies.
Whatever his reasons, Mr Yeltsin has, yet again, dropped a bombshell. With a war in Europe and economic gloom at home, Russia is without a government. The IMF deal will almost certainly founder, and Russia will drift for weeks as the parliament and the Kremlin haggle over a new premier.
A confrontation with parliament, and a possible constitutional crisis, is taking shape as the Duma seems certain to refuse to confirm Mr Yeltsin's nominated candidate for premier, Sergei Stepashin. If it does so three times, then the President must dissolve it, forcing early elections. But the chamber is set to begin impeachment proceedings this week - a move which may also have prompted Mr Yeltsin's decision to fire the popular premier. If it votes in favour - as now seems likely - then it cannot be disbanded. What then happens is not clear.
Yesterday there was widespread condemnation of Mr Primakov's sacking. Only pro-market liberals applauded. Most of the rest of the political spectrum - including the head of the pro-government "Our Home is Russia" - saw it as a serious misjudgement.
The West will also have serious doubts. Mr Primakov was never much loved in Washington, which recoiled at the presence of senior Communists in his government - notably, the First Deputy Prime Minister Yuri Maslyukov (who yesterday announced he would have no part in the next government.)
Nor did his hard-ball, pro-Russian foreign policy, honed in his years as foreign minister, win him many Western fans. His mission to Belgrade at the start of the Yugoslav war went down particularly badly abroad. Soon afterwards Mr Yeltsin handed the Kosovo mediating job to Mr Chernomyrdin.
Yet, in the end, Mr Primakov was respected. He was a tough but pragmatic dealmaker, a safe pair of hands in an unstable and heavily armed nation. The same cannot be said of the increasingly unstable Russian leader who fired him.
Russia's Succession of Prime Ministers
Made acting prime minister by Yeltsin in June 1992 but the parliament refused to confirm him
Voted in by parliament in 1992. For over five years led market reforms marred by bungling and corruption
Appointed by Yeltsin in March 1998. Could do little in the five months before the rouble crashedReuse content