Allies of Kenya's President Uhuru Kenyatta want William Ruto to step down as deputy president because he is "prematurely" campaigning to succeed his boss in the 2022 elections, local media reports say.

Legislators accuse Mr Ruto of regularly holding political rallies and frustrating President Uhuru's Big Four agenda that seeks to provide affordable housing, healthcare, food security and manufacturing, privately owned newspaper The Standard reports.

The Star newspaper says lawmakers have warned Mr Ruto not to visit President Kenyatta's home county of Kiambu unless he is accompanied by the head of state.

Mr Ruto is accused by his critics of defying the president - an allegation he denies.

Mr Kenyatta's two terms as president are due to end in 2022, but there is speculation that he may push to change the constitution so that he can remain in government as an executive prime minister.