Gary Gershoff / WireImage 1 / 8
Gary Gershoff / WireImage 1 / 8

Uma Thurman's former fiance is demanding that he get more visitation rights with the daughter that he and the actress share.

Arpad Busson, who has been off and on with Uma for years, filed a motion for temporary visitation rights in a New York court on August 31, the Daily Mail revealed. Last year, the former couple reached an initial custody agreement for 3-year-old Luna Thurman-Busson. At the time, he said he wanted be able to make more decisions on behalf of his daughter.

Uma representative released a statement after the initial lawsuit was filed, stating, "It is unfortunate that this very private discussion regarding Mr. Busson's visitation rights and his participation in decision making has been made public. However, we are optimistic that a fair agreement for both sides will be reached out of court."

He first filed a custody lawsuit against the "Kill Bill" star in New York in 2014. After a year, the former duo reached a settlement and impressed the judge, who praised them for putting the best interests of their daughter above their displeasure with one another.

What that particular agreement was isn't known, as the terms of the deal were sealed.

It's not clear why he wants to change the settlement now.

In Arpad's new custody lawsuit, he filed a Pendente Lite Visitation, which is generally only filed during an on-going battle, with one person seeking to have the judge award temporary visitation until the outcome of the case.

Generally speaking, once the custody issue is resolved and finalized, the temporary decision is then voided.

A hearing is set for September 29 in New York Supreme Court.

Arpad, a London-based French multimillionaire, began dating Uma in 2007. They eventually got engaged (he gave her an 8-carat diamond ring), but called off the wedding in 2009. They reconciled in 2011 and had Luna the next year. The couple was again engaged but again parted ways shortly after.