Three Britons were kidnapped while entering the southern Gaza Strip from Egypt for reasons unclear, reported Sky News on Wednesday.
Security officials in Gaza said one of the victims is a human rights worker but had no further details. There was no immediate claim of responsibility.
Recent kidnappings of foreigners in Gaza have ended without bloodshed and with the hostages being released unharmed. In most cases, the kidnappers were seeking jobs in the Palestinian security forces, the release of imprisoned relatives or other personal matters.
Abbas' critics have accused him of giving in to kidnappers' demands, thereby encouraging more abductions.
Frank McGinley, a duty officer with the British consulate general in Jerusalem, said his country was investigating the report but had no further comment.