According to newspaper reports on Friday, one of four people arrested while trying to enter Iraq from Syria, named al-Dosari as having helped him in his mission.
Al-Dosari who is spokesman of the Association of Victims of Torture and Arbitrary Arrest, evaded an attempt by security forces to arrest him on Monday, Al-Siyassa daily reported.
However, al-Dosari charged on a website that authorities were after him because he had evidence of human rights violations by security services and was defending victims of abuse.
Several Arab and international human rights groups denounced the failed attempt to arrest al-Dosari and deplored what they called the pressure exerted on "defenders of victims of torture and arbitrary arrest in Kuwait," Al-Siyassa said.
US troops used Kuwait as launch
pad for the invasion of Iraq
The Paris-based Arab Committee for Human Rights (ACHR) has expressed concern over the attempts to arrest al-Dosari.
In a statement received by Aljazeera, ACHR criticised Kuwaiti authorities of targeting al-Dosari.
The statement said al-Dosari had been assaulted and called on Kuwaiti authorities to launch an investigation.
The Geneva-based Karama (Dignity) Association for Defending Human Rights (KADHR), Hague-based Justice Organisation (JO) and the Paris-based Association for Defending and Assisting Defenders of Human Rights (ADADHR) have endorsed the ACHR statement.
The organisations called on the Kuwaiti government to stop what they described as "harassment".
Speaking to Aljazeera, Walid al-Tabtabai, a Kuwaiti Member of Parliament and chief of Parliamentary Committee of Human Rights (PCHR) said the ACHR allegations were true.
Dr Haytham Manaa, the spokesman of the ACHR told Aljazeera the committee had audio and video evidence of torture in Kuwait.
"Pressure on those struggling against torture like al-Dosari must stop", he added.
Meanwhile, Kuwaiti authorities have arrested several people on suspicion of involvement in recruiting youths to fight US occupation forces in Iraq after the extradition of four suspects from Syria.
"Pressure on those struggling against torture like al-Dosari must stop"
Dr Haytham Manaa,
The interior ministry "received from Syrian security authorities four people arrested on charges of illegal entry into Iraq" from the Syrian border, the papers quoted a ministry official as saying late on Thursday.
Ministry spokesman Adil al-Hashash said the four had confessed to the charges and informed on other people, some of whom were detained and found in possession of weapons as well as "maps and plans for (terrorist) operations."
Aboutaaa 25,000 US troops are based in Kuwait, which served as the main launching pad for the US-led invasion last year that ousted Iraqi president Saddam Hussein.