SAN'A, Yemen—Clashes erupted across Yemen’s capital on Monday as Houthi militants demanded a greater say in the crafting of the country’s constitution, days after kidnapping a top presidential aide to leverage their demands. The Houthis are a militant group that represents Yemen’s Zaidi sect—an offshoot of Shiite Islam. In September they forced the government’s resignation after occupying the capital San’a, complaining about the slow pace of reforms undertaken by President Abded Rabbo Mansour Hadi, including the drafting of a new constitution. The militants have since spread across Yemen, occupying some of the country’s most important infrastructure including sea ports, while opposing Mr. Hadi’s attempts at piecing together a new government. In the latest clashes Monday, unknown gunmen fired on the vehicle of the Yemeni prime minister who escaped unhurt, according to Minister of Information Nadia al Sakkaf. Fighting also broke out around the presidential palace. Mr. Hadi has demanded that the Houthis return the presidential chief of staff, Ahmed bin Mubarak, who was kidnapped on Saturday, after forging ahead with a new constitution that would divide Yemen into six federal states, a move opposed by the militants. Yemen is a cornerstone of the U.S. counterterrorism program in the region and Mr. Hadi has worked closely with Washington as it struggles to defeat al Qaeda in the Arabian Peninsula, the organization’s local branch. AQAP claimed responsibility for the Paris attacks on the Charlie Hebdo magazine earlier this month and is considered to be al Qaeda’s most deadly branch with the greatest global reach. If Mr. Hadi is ousted, it could put the U.S. counterterrorism program in Yemen influx. Mr. Hadi personally approves U.S. strikes against the AQAP militants, according to top aides. The Houthis oppose the U.S. program. Osama Sari, a top Houthi official, said that Mr. Hadi was warned numerous times about ignoring Houthi input on the next constitution. “We stressed that we will not allow a constitution that divides Yemen into six states. Hadi knows this is a red line,” Mr. Sari said. Both sides blame each other for the clashes. “The Houthis threatened the president last night and informed him they will attack him directly. This resulted in the president sending hundreds of troops to the street and closing roads leading to the palace,” a presidential source said. WSJ