The move followed a Saudi-led coalition air strike on the southern Yemeni port of Mukalla.
The attack on what Riyadh said was a UAE-linked weapons shipment marked the most significant escalation between Riyadh and Abu Dhabi to date in a widening rift between the two Gulf powers.
In Washington, the US State Department said Secretary of State Marco Rubio spoke with the Saudi and UAE foreign ministers about tensions in Yemen and other issues affecting security in the Middle East.
Several Gulf countries, including Kuwait and Bahrain, said they would support any efforts to bolster dialogue and reach a political solution.
Qatar said the security of Saudi Arabia and other Gulf countries "constitutes an inseparable part" of its own security.
The UAE defence ministry said it had voluntarily ended the mission of its counterterrorism units in Yemen, its only forces still there after it concluded its military presence in 2019.
The ministry said its remaining mission was limited to "specialised personnel as part of counterterrorism efforts, in co-ordination with relevant international partners".
In a statement, it said recent developments had prompted a comprehensive assessment, the state news agency WAM reported.
Saudi Arabia had accused the UAE of pressuring Yemen's separatist Southern Transitional Council (STC) to push towards the kingdom's borders, and declared its national security a "red line".
It was Riyadh's strongest language yet against the UAE in the falling-out between the neighbours, who once co-operated in a coalition against Yemen's Iran-aligned Houthis but whose interests in Yemen have steadily grown apart in recent years.
On Tuesday the coalition struck what it said was a dock used to provide foreign military support to the UAE-backed separatists. The head of Yemen's Saudi-backed presidential council gave Emirati forces an ultimatum of 24 hours to leave.
The UAE said it had been surprised by the air strike, and that the shipments in question did not contain weapons and were destined for the Emirati forces.
But it said it sought a solution "that prevents escalation, based on reliable facts and existing coordination".
Yemen's Saudi-led coalition said a shipment arriving from the United Arab Emirates to Yemen's southern port of Mukalla had containers loaded with weapons and ammunition.
The coalition said it had information that such weapons would be transported and distributed to locations in Yemen's Hadramout.
In a televised speech, Alimi said it had been "definitively confirmed that the United Arab Emirates pressured and directed the STC to undermine and rebel against the authority of the state through military escalation", according to the Yemeni state news agency.
Saudi Arabia and the UAE are both major players in the OPEC oil exporters' group, and any disagreements between them could hamper consensus on oil output.
They and six other OPEC+ members meet online on Sunday, and OPEC+ delegates say they will extend a policy of maintaining first-quarter production unchanged.
Tuesday's airstrike followed the weekend arrival of two ships from the UAE port of Fujairah on Saturday and Sunday without coalition authorisation, the coalition said.
The Saudi state news agency published a video showing a ship it identified as "Greenland" and said arms and combat vehicles were unloaded from the vessel.
The registered owner and operator of the Greenland, a roll-on/roll-off cargo vessel, is Salem Al Makrani Cargo Company, headquartered in Dubai, with a branch in Fujairah, the company website indicates.
The coalition said the strike caused no casualties or collateral damage, according to Saudi state media.
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