Heart-throb and career high: 2000–2005
Abbas appeared in a small role in Hey Ram (2000), which starred Kamal Hassan along with Bollywood stars Shahrukh Khan and Rani Mukerji in the leading role. Dreams (2000), a Malayalam film, was released after Hey Ram (2000), where Abbas appeared with Dileep and Meena. The movie became a flop at the box office. In 2000, Abbas worked with Rajiv Menon's romantic-drama Kandukondain Kandukondain, including an ensemble cast of Mammootty, Ajith Kumar, Aishwarya Rai Bachchan and Tabu. The film became commercially successful and marked the second collaboration of Abbas and Tabu after Kadhal Desam. Abbas then acted in the Telugu film Madhuri (2000) which became a box-office failure.
In 2001, Abbas starred in Minnale, with Reema Sen and R. Madhavan, where he was portrayed as a college rival to Madhavan's character and his role was very much acclaimed. The film went on to become one of the blockbusters of the year. This was the second film of Abbas and Madhavan after the 1998 Kannada film Shanti Shanti Shanti. Abbas made a cameo appearance, portraying himself in Vinnukum Mannukum (2001). He then appeared in N. Lingusamy's directorial debut, the family drama Aanandham (2001), with Mammootty, Murali and Sneha. It was the second collaboration of Abbas and Mammootty after Kandukondain Kandukondain (2000). It became one of the biggest hits of Abbas's career. Abbas' performance in the film was praised by critics. In an interview, he picked Aanandham as his career-best film.
In 2002, Abbas collaborated once again with Kamal Hassan in comedy film Pammal K. Sambandam, where he shared the screen with Simran and Sneha again. In the movie, he played the role of Kamal Hassan's brother. It received positive reviews and became a commercial success. He then collaborated with Vineeth again in romantic drama Nee Premakai (2002), directed by Muppalaneni Shiva, with Laya playing the female lead role in the film. Regarding his performance in the film, a critic wrote, "Abbas simply dominates the show throughout as a cunningly cute contender. He keeps good humour going on with his funny acts". In 2002 he made his debut in Bollywood with Ansh: The Deadly Part. He worked in an ensemble cast alongside Ashutosh Rana, Om Puri, Milind Gunaji, Rajat Bedi, Sharbani Mukherjee, Shama Sikander and Ashish Vidyarthi. The film was not a big success, but its soundtrack composed by Nadeem–Shravan became a hit. After this, two further films, including Aur Phir with Bipasha Basu, were shelved, and he continued to appear in Tamil films in supporting roles through the mid-2000s.
Abbas again collaborated with Kathir for Kadhal Virus (2002), with Richard Rishi and Sridevi Vijaykumar. Unlike his previous two films with the director – Kadhal Desam (1996) and Kadhalar Dhinam (1999) – Kathir's Kadhal Virus was panned by critics and fared poorly at the box office. Abbas then appeared alongside R. Sarathkumar and Sakshi Shivanand in Manasthan (2004), directed by Marumalarchi Bharathi. The film opened to mixed reviews. He again collaborated with Soundarya in Tamil–Kannda horror film Swetha Naagu (2004), which became an average grosser. Abbas played role of a villain in Tamil horror film Shock (2004). He shared an ensemble cast with Prashanth, Meena, Thiagarajan, Suhasini, Kalairani, and Sarath Babu. The film received a positive response from critics and was a box office success. In 2004, he co-starred with Sathyaraj in the action comedy Adi Thadi, which became a super-hit. It was second collaboration of Abbas and Sathyaraj after Malabar Police (1999). He reprised his role in its Telugu remake Political Rowdy (2005), which was not great success like original film. His last release of 2005 was an action-drama movie, Vanakkam Thalaiva.