Sources in the republic's capital, Minsk, told Reuters that Mr Lukashenko, who has been under a barrage of international criticism, had offered to withdraw his bitterly contested new draft of the constitution, only five days before the nation was due to hold its official voting day.
If the deal is confirmed and survives, then MPs seem certain to drop their plans to move to impeach the maverick president, who had been seeking a tranche of autocratic powers including the right to appoint judges, top election officials, and many members of a new, two- chamber legislature.
The possible breakthrough came after Britain, France, Germany and Italy added their voice to the chorus of international condemnation of Mr Lukashenko, whose referendum had been declared illegal by his parliament and constitutional court - bodies which he has routinely ignored.
For months, there have been fears that the 42-year-old president, a former Soviet collective farm director, would bring about a bloody showdown with his parliament, dealing a blow to democracy and spreading ripples of alarm from the Baltics to the Black Sea and beyond.
Fearful that Mr Lukashenko's sizeable security forces may close it down altogether, MPs had occupied parliament round-the-clock in Minsk since Friday. His prime minister, Mikhail Chigir, has resigned in protest over the referendum. According to reports, the president - apparently under pressure from Moscow - said he was willing to compromise after meeting the chairman of the Belarus constitutional court, Valery Tikhinya, one of his fiercest opponents. Earlier, the Belarusan parliament had produced an olive branch of its own, offering to break the deadlock by agreeing to abandon a second, parallel referendum which proposes that the presidency be scrapped, if Mr Lukashenko drops his.
However, despite the glimmer of hope, the West and Russia were expected to greet the news with caution. Moscow is universally seen as the key player in efforts to resolve the crisis as it exerts great influence on the former Soviet republic, which depends on it for gas and oil.
Earlier, a Kremlin spokesman said President Yeltsin and his prime minister, Viktor Chernomyrdin, who met one another for 90 minutes yesterday, were "alarmed by the rising tensions" in Belarus and hoped that "the art of political compromise will replace the ambitions and confrontations among politicians".
Officially, voting day is on Sunday. If the vote still goes ahead, it seems certain to be a foregone conclusion, as there are signs aplenty that the president has little regard for fair play. He has fired the head of the Central Election Commission, Viktor Gonchar, who complained of irregularities among the thousands of absentee ballots that have already been cast.
And for months, he has excluded his opponents from the heavily censored state-run media, whilst using the airwaves to advertise his cause.Yesterday journalists from Russia's three top TV channels, RTR, ORT and NTV, complained that the Belarusan authorities were preventing them sending reports.
Quick guide to Belarus
t President: Alexander Lukashenko, 42, former collective farm director who was elected July 1994, in a wave of rural nostalgia for the return of the Soviet Union. Once spoke admiringly of Hitler.
t Population: 10.3m, of whom 78 per cent are Belarusan, and 13 per cent Russian. Minsk, the dreary Soviet-style capital, has 1.6m residents.
t Location: bordered by Ukraine to the south, Poland to the west, Russia to the east and Lithuania and Latvia to the north. t Forces: The 1,500-strong Presidential Guard is fiercely loyal to their boss. There is a highly active KGB, and a disproportionately large military of 82,000. t Weapons: include 18 former Soviet SS-25 Intercontinental Ballistic missiles, which Belarus is due to return to Russia. It has 349 combat aircraft and 2,348 battle tanks. t National Anthem: the former Soviet one, without the words. History's low point: loss of 25 per cent of the population in the Nazi invasion during the Second World War. t Economy: Grim. Heavy engineering hard-hit in particular by the post- Soviet slump. Depends on Russia for subsidised gas and oil. t Religion: the Orthodox Church is largest church, followed by Roman Catholic. t History's high point: declaring independence on 25 August 1991 and helping bring about the end of the Soviet Union.Reuse content