CAIRO (AP) — Fighting in Yemen's grueling civil war ground on Tuesday, with Houthi rebels saying they halted the advances of their adversaries, the U.S.-backed, Saudi-led Arab coalition seeking to oust them from power.

Combat continued around the key port city of Hodeida, where the Iran-backed Shiite rebels said in an overnight statement that a three-pronged coalition assault had been stopped with heavy fighting around the city's outskirts, acknowledging that they had lost at least 30 men and a dozen armored vehicles.

Dozens of fighters have been killed and hundreds wounded from both sides since the coalition offensive on the city began five days ago, following calls by the Trump administration for a cease-fire by late November. Witnesses have reported dead bodies littering the ground and left inside burnt-out vehicles at the city's edge.

Local media reported that air raids by the coalition were continuing, as was sporadic fighting around Hodeida, especially along 50th street and the 7th of July neighborhoods in the east. Other fronts include the provinces of Dhale and Bayda, to the south, and in the north in Hajjah and Saada, a Houthi stronghold.

The Houthis said in their statement they had also stopped an attempted incursion by "mercenaries of the Saudi army," into Yemen from Jizan, across the border in Saudi Arabia.

Witnesses say several civilians have been killed by shelling in residential areas.

Meanwhile, the Norwegian Refugee Council said millions of Yemenis are edging closer to famine and fatal disease as the Saudi-led coalition's blockade on sea, land and air routes in the Arab world's poorest country continued.

The coalition restricted access to Yemen in November last year after a missile assault by rebels targeted the Saudi capital, Riyadh.

Jan Egeland of the NRC said "the past 12 months have been a never-ending nightmare for Yemeni civilians."

The Saudi-led coalition, which backs the internationally recognized Yemeni government, has been at war with the Houthi rebels since March 2015 in a stalemated conflict that has generated the world's worst humanitarian crisis. Hodeida, the main portal for humanitarian aid to the suffering population, has become the epicenter of the conflict.

The U.S. has sold billions of dollars' worth of arms to Saudi Arabia and provides logistical and other support to the coalition.