Kilome signed a minor-league contract with the Nationals on Monday.
Kilome (undisclosed) has appeared in two games for Triple-A Syracuse since being reinstated from the 7-day injured list Tuesday, covering two scoreless innings while striking out two and allowing no hits and two walks.
Kilome cleared waivers Saturday and was outrighted to the Mets' alternate training site.
Kilome was designated for assignment by the Mets on Saturday.
Kilome was optioned to Triple-A Syracuse on Tuesday.
Kilome was optioned to the Mets' alternate training site Saturday, Tim Healey of Newsday reports.
Kilome (finger) was activated from the 10-day injured list Friday, Tim Healey of Newsday reports.
Kilome was placed on the injured list with a split fingernail, Tim Healey of Newsday reports.
The Mets optioned Kilome to their alternate training site Wednesday, Tim Healey of Newsday reports.
Kilome was optioned to the Mets' alternate training site Tuesday.