DUBAI—Fighting on Monday marred the latest cease-fire in Yemen just hours after it began, dimming prospects for next week’s United Nations-backed talks aimed at ending the yearlong war between Houthi rebels and a Saudi-led military coalition.

Residents of Taiz said the coalition carried out airstrikes on their southern city. Fighting also broke out some 35 miles east of the capital San’a, a witness said. The scope of that violence and the identities of the combatants weren’t immediately known.

Negotiations aimed at ending the war, which the U.N. estimates has killed more than 6,000 people, are set to begin Apr. 18 in Kuwait. Several previous attempts to negotiate an end of the conflict have failed.

The rebels and the Saudi coalition had pledged to comply with the U.N.-mediated cease-fire, which went into effect late Sunday, local time. Ismail Ould Cheikh Ahmed, the U.N. special envoy to Yemen, said both sides were committed to it.

“Now is the time to step back from the brink,” he said. “The progress made represents a real opportunity to rebuild a country that has suffered far too much violence for far too long.”

The cease-fire has been on tenuous footing from the start. Armed Yemeni factions allied with the Saudi coalition near Taiz said earlier this week they wouldn’t abide by the cease-fire.

Yemen’s main jihadist groups, al Qaeda in the Arabian Peninsula and local branches of Islamic State, weren’t expected to honor it, either. AQAP fighters advanced Monday in the southern Abyan province, local officials said.

Several previous truces, including one in December, have collapsed.

In a statement carried by the official Saudi Press Agency, the coalition said Sunday it reserved the right to respond to any violations of the cease-fire.

The coalition, made up mostly of Riyadh’s Sunni Arab allies, began an air campaign in March 2015 to dislodge the Houthis and restore Abed Rabbo Mansour Hadi to the presidency. It later launched a ground campaign.

Riyadh sees the Houthis as a proxy of Shiite Iran, their main rival for power and influence in the Middle East.

Last week, foreign ministers of a Gulf Arab bloc of nations, the Gulf Cooperation Council, voiced concerns about Iranian behavior in Yemen and elsewhere in the region during a meeting with U.S. Secretary of State John Kerry in Bahrain.

“We stressed that if Iran wants to have normal relations with the GCC states, it has to change its policies,” Saudi Foreign Minister Adel al-Jubeir said.

Iran supports the Houthis politically but has denied sending them arms. But several shipments of weapons have been intercepted in the waters near Yemen in recent months, and the U.S. Navy said a cache of arms captured in a fishing boat last month originated in Iran, likely bound for Yemen.

The coalition said the truce would allow aid agencies to deliver emergency medical aid and other relief to war-ravaged areas.

The war has put Yemen, already the Arab world’s poorest country, on the brink of famine, the World Food Program says.