GENEVA -- Fighting in Yemen raged on Tuesday, with dozens reported killed even as the country's Shiite Houthi rebels arrived in Geneva for U.N.-brokered peace talks. U.N. figures reported an increasing number of civilians killed in a conflict that is showing little sign of abating.

The Geneva talks are aimed at ending months of fighting that prompted a Saudi-led coalition to launch an air campaign against the Houthis and their allies nearly three months ago. Still, neither side has shown desire to compromise even as dozens died in renewed fighting in the southern city of Aden.

Following initial meetings with the U.N. envoy, delegate Ghaleb Mutlak said that the rebels are trying to achieve a truce for the Muslim holy month of Ramadan, and that their delegation is willing to stay in Switzerland as long as it takes to end the bloodshed.

U.N. special envoy Ismail Ould Cheikh Ahmed said nothing will be settled unless the two sides can be persuaded to sit down together, but that just getting them both to Geneva was a "great achievement."

"We should not underestimate the significance of this event," he told reporters after meeting with the Houthi delegation. "It is the important start toward the return to a political process. Let us be realistic, it will be a difficult path, but the important issue is that we start addressing the crisis."

Meanwhile on the ground, heavy combat shook the cities of Taiz and Marib, while airstrikes from the Saudi-led coalition hit rebel positions in the capital, Sanaa, as well as Hajja, Saada, al-Jawf and Shabwa province.

The rebel delegation from Sanaa set off Sunday but arrived a day later than expected on Tuesday morning. They blamed the delay on Egypt, claiming they weren't given permission to fly over its airspace, although Cairo denied the charge.

It's unclear how long the talks -- at least initially involving mediators shuttling between the parties, rather than face-to-face encounters -- will last. U.N. spokesman Ahmad Fawzi said the start of Ramadan later this week may affect whether the delegations stay in Geneva.

"It is a golden opportunity to try and resolve this crisis," Fawzi said. "Whether they will agree to extend their stay beyond the beginning of Ramadan is anybody's guess."

Yemen's conflict pits the Houthis -- who seized Sanaa last year -- and military units loyal to former President Ali Abdullah Saleh against an array of forces, including southern separatists, local and tribal militias, Islamic militants and loyalists of exiled President Abed Rabbo Mansour Hadi.

The delegation from Sanaa includes loyalists of Saleh and representatives of other political groups.

U.N. figures released Tuesday underlined the urgency of finding a solution. Between Thursday and Monday, 50 civilians were killed -- among them 18 children -- and a further 111 were wounded, the U.N. human rights office said. That brings the total number of civilians killed since March 26 to 1,412, with 3,423 wounded, it added.

UNICEF, the U.N. children's agency, said at least 279 children have been killed and 402 wounded since March 26, compared with 74 killed and 244 wounded in all of 2014. UNICEF said children are being used by armed groups to man checkpoints or carry arms.

Speaking at an emergency session on Yemen at the headquarters of the Organization of Islamic Cooperation in Jiddah, Saudi Arabia, Hadi reiterated his position that the talks must focus on implementing U.N. Security Council Resolution 2216, which calls on the rebels to lay down their arms, give up captured territory and cease actions undermining the exiled government.

Mohamed Abdallah Alzuberi, a Houthi delegation official, said in Geneva that "there can be no consultation with those who are not legitimate."

"As a political power inside Yemen, we have agreed that the (current) head of the government is not part of the dialogue, as we are the ones who should be choosing the head of the government," he said.

U.N. Secretary-General Ban Ki-moon pressed for a halt to fighting at the start of Ramadan, the Muslim month of dawn-to-dusk fasting, as he launched the talks Monday.

"Our ambition is for a truce to happen over Ramadan, but a truce isn't enough. We want to solve the problem and stop the aggression," Alzuberi said.

On Monday, the exiled government's foreign minister, Riad Yassin, said such a limited cease-fire "has to run parallel to the withdrawal of Houthi militias and those of Saleh from all cities and governorates of Yemen."

Meanwhile, security and medical officials said a passenger bus carrying families fleeing the violence in Aden was hit by an airstrike killing more than two dozen civilians. They spoke on condition of anonymity because they were not authorized to brief journalists.

Houthi leader Abdul-Malek al-Houthi lambasted the war as a "grave aggression" that was killing women and children and destroying the country to serve the interests of Saudi Arabia, the U.S., and Israel.

"They want this country to be under their hegemony, and they want instability to keep the country under their control," he said in a defiant speech broadcast on Houthi-run Al-Masirah television.

Security and medical officials said a passenger bus carrying families fleeing the violence in Aden was hit by an airstrike killing more than two dozen civilians. They spoke on condition of anonymity because they were not authorized to brief journalists.

- David Rising and Geir Moulson in Berlin and Brian Rohan in Cairo contributed to this report.