what was the cause of his regert and remorse of ali
Answers
Many Sunni references point to the fact that Ayesha, along with some of the companions of the Prophet (saws) such as Talha and Zubair engaged into a battle with Ali (a.s).
References :
History of Ibn al-Athir, v3, page 120
Usdul Ghabah, v2, page 252
Al-Mustadrak by Al-Hakim,
The fighting was instigated by Sab'iyyah, it was not the intention of Ali or A'ishah.
The historians like al-Tabari (that you referred in the question) and others mention that this fighting was instigated by a group known as the Sab'iyyah in order to prevent the conciliation between the companions.
After the killing of Uthman, some companions wanted the murderers to be brought to justice. On the other hand Ali wanted to stabilize the situation and avoid an even bigger problems. So he chose not to immediately. A'ishah, Talha, and Azubayr lead a contingent to Basra (May Allah be pleased with them all) with the intention of reconciliation.
When Ali heard this, he traveled to meet them with an a large contingent. The intention was to make them understand and obey his order (as the caliph and leader of Muslims), as well as discussing what to do with the murderers.
The Sab'iyah saw this as a threat to themselves. They hid among both sides. When the two met they caused them fight: They would attack the other side. Those in the other side would call out that they are being attacked. This is how the battle started and a number of great companions died.