He said that if the 24-hour walkout went ahead a proposed deal on jobs and safety would be withdrawn.
The Rail and Maritime Transport Union (RMT) is calling the strike over the government's planned partial privatisation of the tube.
It fears safety will be affected by the action and jobs will be lost.
Mr Monks has been involved in lengthy talks between the RMT and London Underground. A proposed agreement was reached but the rail union's executive decided last night that it fell short of the guarantees it was seeking.
In a letter to the RMT, Mr Monks said that "very considerable progress" was made during the talks and warned that if the strike went ahead an agreement already accepted by the driver's union, Aslef, would be withdrawn.
He invited the RMT executive to meet the TUC executive to try to find a way of resolving the dispute.
"In the meantime, however, to enable these discussions to take place with any chance of success, I would formally request the RMT's executive committee to suspend the industrial action," he said.
Related articles
02.05.01, Bob Kiley: "I am losing my battle to save the tube"
02.05.01: Talks fail to avert tube strike
28.04.01: 'Regrets for 30 years' if Prescott presses ahead with tube contracts
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The government's plans for a public-private partnership
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