In his closing argument, Reiser, who is acting as his own attorney, told the jury that his 12-year-old son Rory and 11-year-old daughter Niorline "need someone who believes in them and their success."
Reiser, 48, a computer engineer who owned a software company, said of himself and his children, "If we were a team, we could build a business."
"There are things I'd like to pass on to my kids that could be worth money," he added.
Reiser is serving a term of 15 years to life in state prison for killing his wife, 31-year-old Nina Reiser, on Sept. 3, 2006.
His children have been living in Russia, where Nina was born and raised, with their grandmother since December 2006.
The children's attorney, Arturo Gonzalez, is asking jurors to award $10 million in damages to each child, plus an additional $5 million in punitive damages.
Gonzalez said he agrees with Reiser that his children need compassion and caring. However, Gonzalez said, "they had it, but Mr. Reiser took it away" by killing their mother.
Gonzalez said it's not clear whether Reiser has any assets now, but that he wants jurors to award damages to Reiser's children because he thinks Reiser might be able to come up with valuable ideas while in prison because of his background in the computer industry.
Reiser said again this morning that the reason he killed his wife was to prevent her from harming their children. He has admitted that there was no physical abuse but said she was harming them in other ways.
He said in the trial that Nina convinced a number of health professionals to invent illnesses in the children that could be blamed on him so she could have custody of them after she filed for divorce in 2004.
Jurors began their deliberations at about 11 a.m. Monday.