Although there is no federal rule expressly allowing motions to reconsider, parties file them anyway. Some evidence is that the PACER electronic filing system allows you to categorize a motion as one "for reconsideration."
A body of case law describes when motions to reconsider are appropriate. Following is a section from a brief (not mine) that quotes from a number of Illinois cases on the issue:
A motion to reconsider is available to correct manifest errors of law and fact, or to present newly discovered evidence. Wolves v. National Railroad Passenger Corp., 1990 WL 84519, at *1 (N.D. Ill. 1990) (not reported in F. Supp.) (citing Publisher's Resource Inc. v. Walker-David Publications, Inc., 726 F.2d 557, 561 (7th Cir. 1985)). A motion to reconsider should be used neither to introduce new evidence that was available during original consideration, nor to introduce new legal theories. Calderon v. Reno, 56 F.Supp.2d 997, 998 (N.D. Ill. 1999) (citing Publisher's Resource, 762 F.2d at 561)).
A motion to reconsider a remand order is proper "where the court has patently misunderstood a party, or has made a decision outside the adversarial issues presented to the Court by the parties, which made an error not of reasoning but of apprehension." Calderon, 56 F.Supp. 2d at 999 (citing Bank of Waunake v. Rochester Cheese Sales, Inc., 906 F.2d 1185, 1191 (7th Cir. 1990)). "A further basis for a motion to reconsider would be a controlling or significant change in the law or facts since the submission of the issue to the Court." State Bank of India v. Commercial Steel Corp., 2001 WL 423001, at *2 (N.D.Ill. 2001) (not reported in F.Supp.2d). "Such problems rarely arise and the motion to reconsider should be equally rare." State Bank of India v. Commercial Steel Corp., 2001 WL 423001, at *2 (N.D.Ill. 2001) (not reported in F.Supp.2d) (citing Rounds v. City of Chicago, No. 94 C. 1708, 1996 WL 99408, at *1 (N.D. Ill. March 5, 1996) (citations omitted), aff'd, 95 F.3d 1154 (7th Cir. 1996)).
That's a pretty good description of the circumstances under which a motion to reconsider might be appropriate, and I wanted to bookmark it here for future use.

Unfortunately, a motion for en banc rehearing, like a motion for reconsideration, sends a strong signal that, in the opinion of the movant, the judges got something flat wrong. Not just arguably wrong, or subtly wrong, but glaringly wrong. As such, it makes an implicit statement - hard to avoid - that the judge should be ashamed of their decision. I conjecture that it is therefore _much_ less likely to be granted than a motion for reargument based on new allegedly controlling precedent.
Translation: I recently saw a motion for reconsideration get bounced by a circuit court, and expect that the motion for en banc rehearing will be similarly bounced.
Posted by: Eh Nonymous | September 19, 2005 at 11:44 AM
Evan
I believe that each district makes its own list of "events" for electronic filing and they are not all the same - the list for the S.D. Ohio is not the same as for the W.D. Va. is not the same as for the E.D. Tenn. (the only three places I'm registered).
I suspect, however, they all provide for reconsideration motions.
Posted by: Steve | September 19, 2005 at 05:40 PM
Steve: That makes sense. My comment was based on the Southern District of Illinois and the Eastern District of Missouri.
Posted by: Evan | September 19, 2005 at 07:00 PM
I am not a lawyer but my wife and I have been handling a case pro se. We filed a fifth amended counterclaim in state court (AR) to name the parties involved. Our adversaries immediately jumped on this and called the parties 'separate third party defendants' and filed in federal court and got our case thrown out without even a hearing. We planned to ask the fed judge for reconsideration. Our adversary is a municipality and fight is three years old.
Posted by: Richard Watkins | October 29, 2009 at 06:50 AM
Thanks for great blog....
Posted by: Haji Ghulam Ahmed Bilour | December 04, 2009 at 05:10 AM
We filed a reconsideration pro se and requested the Court to asssent to a summary of facts from the hearing as part of the reconsideration. Our hope was to develop a record of facts for appeal but the Judge denied the motion and ignored our requrest tp a stipulation of facts. Is there a motion for requesting a ruling for stipulating facts?
Posted by: Ralph Nicosia-Rusin | June 26, 2010 at 03:16 AM
Late in seeing your post but as one who's dealt with this: the federal courts actually treat these motions as a mis-labeled motion falling under one of their rules. Which makes sense because substance, not caption, controls.
So if it's after a trial, they review as a motion for new trial. If it's an attack on some other ruling they made, they treat it as a 59(e) motion. (If it's an untimely 59(e) motion, they review it under 60(b)).
I was interested by your citations. I'd note, in the context of your quoted cases regarding remand orders, the plaintiff lawyers out there could make a counter-argument: once a remand order is entered, no matter how wrong, if it's facially on a statutory ground then the federal courts lose jurisdiction to reconsider it (e.g., Thermtron). Just a thought though.
Posted by: Bob | August 04, 2010 at 10:32 PM