CAIRO — Saudi Arabia is emerging at the forefront of a forceful effort by Persian Gulf monarchies to back Egypt’s new military leaders, exacerbating a fierce struggle for influence in the chaotic and increasingly leaderless Arab world and putting the Saudis at odds with the United States, a long-standing ally.

On Monday, Saudi Arabia promised to compensate Egypt for any aid that Western countries might withdraw in response to the harsh tactics employed by Egypt’s leaders to quell protests by supporters of the country’s deposed president, in which nearly 1,000 people and more than 100 police officers are reported to have been killed.