He also invited both Congress leaders to his oath-taking ceremony scheduled to be held in Bengaluru on Wednesday.
Before the meeting, Kumaraswamy told the media that the Congress-JDS combine will give a stable government in Karnataka.
The JDS leader has already indicated that there won't be a rotational arrangement with Congress for the post of the chief minister.
According to sources, there is a proposal to have two deputy chief ministers to strike a balance between the two parties. Congress's G Parameshwara is frontrunner for the deputy chief minister's post.
He earlier met BSP chief Mayawati here and discussed plans of putting in place a Congress-JDS government. The JDS contested the Karnataka election in a pre-poll alliance with the BSP and later had a post-poll tie-up with the Congress.
Many regional party leaders including Delhi chief minister Arvind Kejriwal are likely to attend the swearing-in ceremony.
Kumaraswamy has also invited Telangana Chief Minister K. Chandrashekar Rao, Andhra Pradesh Chief Minister N. Chandrababu Naidu and West Bengal Chief Minister Mamata Banerjee to attend his swearing-in ceremony on May 23.
BS Yeddyurappa had on Saturday stepped down as the chief minister without facing the floor test in the state assembly as the BJP fell short of numbers, following which Kumaraswamy was invited to form the government by Governor Vajubhai Vala.
The JD-S (36) and Congress (78) alliance has 117 members in the House. With the support of three others, Kumaraswamy has 6 more than the required 111 halfway mark, excluding the Speaker to prove a majority in the House.
This is the second time Kumaraswamy, the son of JD-S supremo and former Prime Minister H.D. Deve Gowda, will be the Chief Minister of the southern state, 12 years after the JD-S formed a coalition government with the BJP on February 4, 2006 and remained in office for 20 months till October 9, 2007.
(With additional inputs from agencies)