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Saudi Arabia has enacted a partial ceasefire in Yemen, which comes after its adversaries in the war-torn country - Houthi rebels - announced a surprise truce last week, according to media reports.

The new ceasefire will cover four areas in Yemen - including the capital Sanaa - The Wall Street Journal reported on Friday.

There is the prospect of the truce being widened if the peace holds, following an announcement last week by Houthi rebels that it would put on hold attacks on Saudi Arabia.

So far, two rockets have been fired into the kingdom from Yemen, but Saudi officials do not believe this was a serious infraction of the truce, according to the business daily.

The Houthis appear sceptical about the truce, but have said their ceasefire still stands despite Saudi airstrikes.

"A complete cessation is required," Ahmed Al-Moayed, from the Houthis media office told the daily.

"Otherwise it is manipulation and an attempt to overcome international and humanitarian pressures."

The Houthis' ceasefire comes after attacks on oil facilities in Saudi Arabia, caused tensions to surge in the region.

The Yemen rebels claimed the attack, but the US, Saudi Arabia and some European countries believe the sophistication of the strikes - allegedly using drones and cruise missiles - meant that Iran is the most likely suspect.

Although the Houthis have carried out a number of rocket attacks on Saudi Arabia, they are said to lack the technology required for such pin-point attacks of this nature.

The attacks and Houthis' claim of responsibility led to a rift in the leadership, with some wanting distance with Tehran, according to the Wall Street Journal.

Yemen's war intensified in March 2014 following the intervention of a Saudi-led coalition in the war.

Air strikes, disease and fighting since then has killed tens of thousands of people, the vast majority civilians.