The fresh raids broke a brief lull after the coalition announced last night that the first phase of its "successful" bombing campaign had finished and that it was now focusing on political efforts.
However, the coalition had warned it stood ready to counter any advance by the Iran-backed Huthi rebels and their allies.
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Clashes between the rebels and loyalists left dozens dead and wounded in a string of battleground towns, including second city Aden, an army officer said.
In their first statement since the coalition announcement, the Shiite rebels demanded a complete halt to attacks as a condition for UN-sponsored talks.
"We demand, after a complete end to the aggression against Yemen and the lifting of the blockade, to resume political dialogue... Under the sponsorship of the United Nations," said spokesman Mohammed Abdulsalam.
The Saudi ambassador to the US reiterated that "if the Huthis or their allies make any aggressive moves there will be a response".
The UN had sponsored a Gulf-brokered peace deal that eased former president Ali Abdullah Saleh out of office in 2012, ending a year of bloody protests against his three-decade rule.
UN Secretary General Ban Ki-moon appealed for an end to the fighting and offered the "diplomatic facilities through which we can resolve this issue through dialogue".
Ban said he had proposed a successor to UN envoy Jamal Benomar, who resigned last week after reportedly losing support among Gulf countries.
The World Health Organization says at least 944 people have been killed in Yemen since March 19.
Riyadh said the strikes, which it launched on March 26 as the rebels closed in on Hadi's last refuge in Aden, had succeeded in eliminating the threat posed to Saudi Arabia and its neighbours by the rebels' air and missile capabilities.
But rebels remain in control of Sanaa and swathes of the country while Hadi is in exile in Riyadh, where he fled when the raids began.
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