"We came to Kuwait to ensure implementation of UN [Security Council] Resolution 2216, not to form a unity government," al-Alimi said in a series of tweets cited by Yemen’s official news agency.
"We are not here to reward those who undermined the political path process and violated Yemen’s national consensus," he added, referring to the Houthis and their allies.
"Our position is clear," al-Alimi asserted. "We’re here to reverse the [Houthi] coup and its consequences and restore the political process by hammering out a new constitution before conducting elections."
He went on to cite six preconditions, which, he said, "would not be conceded the Yemeni people".
These include a complete Houthi withdrawal from occupied cities; laying down their arms; the restoration of state institutions; the release of captives; the exclusion of what he described as "obstructionists" from the political process; and the dissolution of non-state militias.
Yemen has been racked by chaos since late 2014, when the Houthis and their allies overran capital Sanaa and other parts of the country, forcing President Abd Rabbuh Mansour Hadi and his Saudi-backed government to temporarily flee to Riyadh.
In March of last year, Saudi Arabia and its Arab allies launched a massive military campaign in Yemen aimed at reversing Houthi gains and restoring Hadi’s embattled government.
This April, the Yemeni government and the Houthis entered into UN-sponsored peace talks in Kuwait aimed at resolving the conflict, in which, according to UN figures, more than 6,400 people have been killed and another 2.5 million forced to flee their homes.