CAIRO — Syrian opposition groups struggled to form a united leadership Tuesday at a meeting in Cairo that exposed the vast disagreements that have prevented them from effectively leading the uprising against President Bashar Assad.

The conference ended late Tuesday with an agreement on two documents, both of them vague. One provides a general outline to guide the opposition through a transitional period, while the other lays out the fundamental principles envisioned for a post-Assad Syria.

The delegates agreed in general terms on support for the Free Syrian Army, the dissolution of the ruling Ba’ath Party, and the exclusion of Assad or other senior regime figures from a place in the transition.

But they failed to reach an agreement on forming a unified body to represent the opposition.

Arguments were rife among the roughly 250 conference participants over key questions, including whether to ask for foreign military intervention to halt the violence and what role religion would play in a post-Assad Syria.

In other developments Tuesday, Assad told a Turkish newspaper that he regretted that Syria shot down a Turkish warplane last month, and a US-based human rights group said the Damascus regime was running a network of torture centers across the country, citing victims’ accounts of beatings, sexual assaults, and electric shocks.

Opposition group members interviewed at the Cairo conference by the Associated Press brought into sharp relief their vast disagreements on issues not addressed in the draft charter, suggesting it papered over the divisions that have prevented them from presenting a united front to the international community.

‘‘It’s very dangerous at this point,’’ said Abdel-Aziz al-Khayyar, who spent 14 years in Syrian prisons and is now part of the Syrian National Coordination Body. ‘‘If we fail to unify as the opposition, it is the greatest gift to the regime.’’

Since the March 2011 start of the uprising that activists say has killed about 14,000 people, Syrian exiles have organized scores of organizations to collect aid, distribute information, and lobby the international community. But all along, infighting has hampered their ability to court international support. And most groups are led by exiles who have lived outside Syria for years, giving them little credibility with activists inside the country.

Indeed, many inside Syria resent the exile leadership, saying they have taken the glory without sacrificing to face the regime.