"Should the blockade continue, we know what (targets) would cause great pain and how to reach them", he said in a speech broadcast on the rebels' Al-Masirah television, in an implicit warning of fresh missile attacks.
"The prime minister made clear that the flow of commercial supplies... must be resumed if we are to avert a humanitarian catastrophe", May's office said.
"They agreed that steps needed to be taken as a matter of urgency to address this and that they would take forward more detailed discussions on how this could be achieved", a Downing Street spokesperson said. The coalition has launched thousands of air strikes against the Houthis who still control much of Yemen's main population centres including the capital Sanaa and the strategic port and city of Hodeidah.
The conflict has claimed more than 8,600 lives since the Saudi-led coalition joined the government's war against the rebel alliance.
Yemen's defenseless people have been under massive attacks by the coalition for almost three years but Riyadh has reached none of its objectives in Yemen so far.
United Nations officials have warned that Yemen faces the risk of the "world's worst starvation in many decades".
Saudi Arabia has accused Iran of supplying the Huthis with arms.
British Prime Minister Theresa May warned against Iran's "destabilizing regional behavior" during a visit to Saudi Arabia.
A spokesman for the Saudi-led military coalition fighting the Huthis in Yemen did not immediately respond to a request for comment. Tehran denies the charge. With the defeat of the Islamic State group, and the backing of three major parties in Syria: Russia, Iran, and now Turkey, Assad is poised to win the long and bloody conflict.
When challenged over the tweet, he then plunged deeper into controversy by suggesting May focus on defending Britain rather than criticising him.