Israel says it has carried out strikes against Houthi military targets in Yemen's capital Sanaa.

The attacks happened after the Iranian-backed militants said they fired a ballistic missile towards Israel on Friday.

The Israel Defence Forces (IDF) said on Sunday it struck the regime's "military infrastructure", including a site "in which the presidency palace is located, the Asar and Hizaz power plants, and a site for storing fuel".

The IDF also said the strikes were carried out in response to "repeated attacks" by the Houthis against Israel, such as "the launching of surface-to-surface missiles and UAVs (Unmanned Aerial Vehicles) toward Israeli territory in recent days".

The presidential palace is within a military site where the Houthi regime operates, and the power plants were used as a "significant electricity supply facility for military activities", the IDF added.

The Houthi-run health ministry said that at least two people were killed and 35 others were wounded.

Referring to the missile fired at Israel on Friday, an Israeli air force official said the weapon most likely carried several sub-munitions "intended to be detonated upon impact".

"This is the first time that this kind of missile has been launched from Yemen", the official said.

The Israeli strikes were the first to hit Yemen since a week ago, when Israel said it targeted energy infrastructure it believed was used by the rebels.

On Sunday, residents in Sanaa said they heard loud explosions near a closed military academy and the presidential palace.

They said they saw smoke plumes near Sabeen Square, a central gathering place in the capital.

"The sound of explosions were very strong," said Hussein Mohamed, a Yemeni resident, who lives close to the presidential palace.

Another resident, Ahmed al Mekhlafy, also said he felt the force of the strikes. "The house was rocked, and the windows were shattered," he said.

Nasruddin Amer, deputy head of the Houthi media office, claimed the Israeli strikes will not deter the rebels, and vowed to continue their attacks on Israel.

Israeli military strikes Houthi regime in Yemen after 'repeated attacks'