Kumar spoke exclusively to VOA Correspondent Steve Herman aboard a commercial flight taking him to Kathmandu.
Nepal's government has been under growing pressure from former Maoist rebels, who won national elections in 2008, but quit the government last year over terms of a peace agreement.
Kumar told Correspondent Herman he is willing to leave his post if it will help expedite the peace process in Nepal, including the drafting of a new constitution, which is mandated by May 28th.
Mr. Kumar said: "If someone comes forward and there's an understanding over any questions then it's better that there be a national consensus government involving all the people."
Thousands of Maoist supporters are now in the capital preparing for a May Day protest that the former rebels promise will be peaceful.
The decade-long civil war in Nepal ended in 2006 with a peace agreement that brought the Maoists into the political mainstream, leading to the formation of a democratic republic and the toppling of the country's 250-year old monarchy.
A full report on Mr. Kumar's interview is being broadcast on the Voice of America and can be found on the VOA website: www.voanews.com/english/news/asia/Nepals-Prime-Minister-tells-VOA-of-Willingness-to-Resign-92490009.html.
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