A man looks at a damaged car at the site of a bombing which targeted Yemen’s Saba News Agency in Sanaa, Yemen June 25, 2015. REUTERS/Mohamed al-Sayaghi

SANAA (Reuters) - A car bomb claimed by Islamic State exploded in the Yemeni capital Sanaa overnight, medics said, wounding at least 28 people gathered to mourn another attack earlier this month.

In a new sign that three months of war in Yemen was ratcheting up, the country's military spokesman said its forces had launched a Scud missile at a Saudi military base on Tuesday.

A Saudi-led military alliance has been bombing Yemen's dominant Houthi group and its allies in the army to dislodge them from the capital and restore the exiled president.

A sectarian-tinged conflict has raged throughout Yemen's south and center, pitting the Shi'ite Muslim Houthis against mostly Sunni local militiamen who support the Arab intervention.

The political vacuum has given hardline Sunni militants greater room to operate. They regard the Houthis as apostates worthy of death, and the overnight blast was the latest in a series of attacks on the group and their supporters.

"The explosion was caused by a car bomb which exploded behind the military hospital in the Sha'oub district in Sanaa, which injured 28 people including 12 women in a building where victims of a previous attack were being mourned," a medical source said.

In a statement posted online, Islamic State claimed responsibility for the blast, saying it had targeted the area "out of revenge for the Muslims against the Houthi apostates."

Despite the months of Arab air strikes backing up the Houthis' armed opponents in Yemen, the Houthis have not lost ground on the battlefield and have stepped up their exchanges of artillery and rocket fire with Saudi forces along their border.

Yemeni forces launched a Scud missile at a missile base in Saudi Arabia on Tuesday, Yemeni state news agency Saba quoted the military's spokesman as saying.

"The rocket units in our heroic armed forces today launched a Scud missile at the Al Sulayyil missile base in Riyadh province ... it comes as a response to the crimes of the brutal Saudi aggression," Brigadier General Sharaf Luqman said.

Luqman said the attack hit the base, which is about 450 km (280 miles) south of the Saudi capital Riyadh, but a previous Scud launched by Yemen's forces earlier this month was shot down by Saudi patriot missiles despite Yemeni claims it struck its target.