RINDGE, N.H. — Democratic incumbent Jeanne Shaheen and GOP challenger Scott Brown yesterday engaged in long-distance warfare in their U.S. Senate battle as Shaheen launched a new attack on Brown but refused to do it face-to-face.

Brown, the former Massachusetts senator, appeared at Franklin Pierce University for what was originally slated as a Senate faceoff, one of several election debates co-sponsored by the Marlin Fitzwater Center for Communication, but he ended up being alone on stage because Shaheen had declined to show up.

“I am disappointed,” Brown said in a talk to first-time voters.

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Shaheen also is refusing to appear on stage with Brown in another planned debate next month sponsored by the Manchester and Nashua Chambers of Commerce, debate organizers reportedly confirmed yesterday.

The New Hampshire Democrat instead chose to launch another trip around the state yesterday, this one called “A Senator New Hampshire Women Can Trust” tour aimed at focusing on Brown’s votes on abortion rights and other issues.

Brown accused Shaheen of running a “desperate” smear campaign.

Shaheen has agreed to three televised debates with Brown but no more.