Martin had earlier said he would call an election if he lost the budget vote.
"Today is one of those more difficult days when it falls to the leader of the opposition to tell the prime minister and the government that they cannot carry on. It is time, for God's sake, to go," Conservative leader Stephen Harper told Parliament.
Harper said Parliament did not have confidence in the Liberals because of government corruption, fiscal irresponsibility and undemocratic action.
He presented his own motion to shut down the House of Commons for the day. He said this would be a new signal to the country and to the governor-general, who represents head of state Queen Elizabeth, that the government has lost the confidence of Parliament.
The House passed the motion overwhelmingly, but only because the Liberals smilingly voted in favour to demonstrate their contention that it was a purely procedural move.
The Conservatives said they were considering continuing to try to shut down the House with similar motions until the Liberals present a confidence motion that would trigger an election.
If the Liberals hold on till 19 May and if they lose the budget vote, the likely result will be an early summer election - just one year after the last one reduced the Liberals to a minority.
Martin made his offer for a vote on his budget the day after the House of Commons approved a censure motion, which the Conservatives and Bloc Quebecois said was, in effect, a confidence vote. Martin disagreed, saying it was a procedural motion.
The government has been badly tainted by a scandal involving allegations of kickbacks to the Liberal Party in return for government contracts. Opposition parties say the Liberals no longer have the moral authority to run the country.
Harper (C seated) has called on
Martin and the Liberals to resign
"On Thursday, 19 May, I will be in Ottawa. I am proposing that there will be on that day a vote on the budget bill and that vote will be a matter of confidence," Martin said.
"If the government loses the vote next Thursday I will seek the dissolution of Parliament," he told reporters.
Any vote will be tight, since the Liberals and their allies only narrowly lost Tuesday's vote on a motion that instructed a parliamentary committee to recommend the government resign.
The government was defeated 153 to 150 but two Liberal ministers and an independent legislator were absent. If all three back the government next week the result would be a tie, leaving the Liberal speaker with the deciding vote.
Harper accused Martin of wanting to wait until next week in the hope that the condition of sick legislators would worsen and they would not be able to vote against the Liberals.
Canadian elections may be called
as early as mid-summer 2005
Pressing the point, two cancer-ridden Conservatives asked the government why Martin would not allow an immediate vote.
"Is he hoping that some of us may not be able to make it?" a sallow Darrel Stinson asked.
Senior Liberal minister Tony Valeri shot back by attacking Harper for suggesting Martin was waiting for deterioration in the health of Stinson and Conservative Dave Chatters.
"The leader of the opposition has shown in fact how low he is prepared to go by suggesting that anyone would take advantage of someone's illness," he said.
Valeri said it was reasonable to expect Parliament to hold a vote next week. "Mr. Harper can't seem to take yes for an answer," he told reporters.
Opinion polls show the Conservatives have only a mixed chance of ending 12 years of Liberal rule if an election were held today, at best forging a minority of their own.
A Strategic Counsel poll for the Globe and Mail newspaper on Wednesday showed the Conservatives had 31 percent support, compared with 27 percent for the Liberals.
But a Decima poll for CanWest newspapers put the Liberals at 37 percent and the Conservatives at 28 percent.