Ismail Omar Guelleh said the war in Yemen, on the other side of a narrow sea channel from the Horn of African nation of Djibouti, was bolstering Al-Qaeda's franchise in the country and posing wider risks for the region.
Guelleh also warned the violence could allow the Yemen-based Al-Qaeda in the Arabian Peninsula (AQAP) franchise to expand its power and control.
AQAP "is taking advantage of these renewed tensions between Sunnis and Shiites... this may create a big gap between Yemeni people, who had never felt the difference between the two communities," Guelleh said in an interview at the presidential palace in Djibouti.
AQAP chief Nasser al-Wuhayshi
In late March, a Saudi-led coalition began air strikes against yemen, after the insurgents, who are backed by ex-soldiers loyal to former president Ali Abdullah Saleh, seized control of large parts of Yemen.
The fighting in Yemen has already sent thousands fleeing across the sea to Djibouti, with many more expected.
"Our borders remain open, they have always been," said Guelleh, president since 1999 of the strategic former French colony, whose port guards the entrance to the Red Sea and Suez Canal.
At its narrowest point, there are only some 30 kilometres (20 miles) between Djibouti and Yemen, across the Bab al-Mandeb strait, the key shipping channel that separates Africa from Arabia.
Djibouti's government aid agency and the UN refugee agency are preparing for some 15,000 Yemenis to arrive by boat in the coming months, making the dangerous crossing across the Gulf of Aden.
Djibouti is already stretched with the refugees it hosts: the tiny nation of 850,000 has taken in some 28,000 refugees, mainly from Somalia.
"This is the third flood of refugees from Yemen after 1986 and 1994, we are used to it," said Guelleh, pointing out that the two neighbors shared close cultural ties and long-standing trade links.
In a volatile region, Djibouti hopes to build a reputation of stability and security.
It has sent troops to join the African Union force fighting Al-Qaeda-affiliated Shebab insurgents in neighbouring Somalia. Last year, Shebab retaliated with the first-ever suicide bombing on Djiboutian soil, targeting a restaurant in the capital popular with foreigners.
Home to the main port used by neighboring landlocked Ethiopia, Djibouti is situated on one of the world's busiest shipping lanes and also hosts several foreign military bases, including from the United States, France and Japan.
Guelleh does not exclude allowing China to set up a military base too, raising the prospect of the US and China having neighboring facilities in the tiny nation.
Djibouti is already home to the only permanent US base in Africa, Camp Lemonnier, which is used for covert, anti-terror and other operations in Yemen, Somalia and elsewhere