Mr. Kabila held about 55 percent of the vote Monday, after Congo's electoral commission released results from 78 of 169 constituencies.
The president is ahead of his nearest rival, Vice President Jean-Pierre Bemba.
Thirty-two presidential candidates and nearly 10,000 parliamentary hopefuls competed in the July 30 election.
A presidential candidate must win more than half the votes cast to avoid a runoff in late October.
Early results show a divide in the country, with Mr. Kabila proving popular in the Swahili-speaking east, but being largely rejected by the Lingala-speaking west, the home of Mr. Bemba.
Election officials expect a preliminary nationwide tally by August 20.
The international community hopes the elections will usher in a new era of democracy for the country after decades of dictatorship and war. However, some of the presidential candidates say the polls were marred by fraud.