He telephoned the Republican House speaker, Dennis Hastert, who agreed to cancel the vote.
The draft had urged the president to show "appropriate understanding and sensitivity" toward events in the Ottoman Empire eight decades ago.
It described the "the systematic and deliberate annihilation of 1.5 million Armenians" as genocide.
According to resolution sponsors, another 500,000 Armenians were driven from their homes.
But Turkey has always said that events in the northeast of the country between 1915 and 1923 cannot be described as genocide.
It says both sides suffered during partisan fighting as the Ottoman Empire collapsed.
Fierce opposition
Such was the concern in the White House - not only about the diplomatic repercussions with Ankara, but the possible impact across the Middle East - that President Clinton personally intervened.
He telephoned the Republican House speaker, Dennis Hastert, who agreed to cancel the vote.
The Turkish Government, a key Nato military ally of the United States, has been fiercely opposed to the resolution, threatening retaliation if it was passed.
Washington was warned that US military aircraft using Turkey's Incirlik air base to patrol the no-fly zone in northern Iraq would be grounded.
There were also fears that Turkey might withdraw from a possible $4.5bn defence deal with an American contractor.
The BBC's Nick Bryant in Washington says Republican leaders in Congress had been under fierce pressure from members, whose home districts harbour large Armenian constituencies.
House speaker Hastert said that although he personally supported the resolution, he believed that the president's request should be heeded.
"The Congress, while it has a right to express its opinions on critical issues of the day, also must be cognizant of the consequences of the expression of those opinions," he said.
The French National Assembly recognised the genocide on 29 May, although the French Government did not endorse the move.
Turkey warned of dire consequences, but the issue blew over.