Citizens of Ayodhya rejoiced over Dasaratha’s choice of Rama as his successor. Dasaratha said to Rama, that since He (Rama) was the son of his (Dasaratha’s) first wife, He had been chosen to be the future king of Ayodhya. So Dasaratha referred to Rama being the eldest of his sons and also the son of his senior-most queen. The rule regarding succession was that the eldest son should be king after his father, said Navalpakkam Vasudevachariar, in a discourse.
It was possible that someone might raise a question about whether this meant that the first son should be king, or the son born to the chief queen should be king. So to keep people from asking such questions, Dasaratha referred to Rama as his eldest son, and as the son of his chief queen. Dasaratha told Rama that he wanted to celebrate Rama’s anointment when Bharata was away. Not that Bharata would be jealous of Rama. Bharata was devoted to Rama, besides being a virtuous man himself. But when it came to power, there was always the possibility that even a righteous person might do something regrettable.
There was another reason for Dasaratha wanting to celebrate Rama’s coronation soon. When he had married Kaikeyi, Dasaratha told her father Asvapathi that Kaikeyi’s son would be made king of Ayodhya. Dasaratha had not made a promise but mentioned such a possibility. At that time, Kausalya had no sons. So Dasaratha might have thought that in case Kaikeyi should have a son first, he could become king. But Rama was born to Kausalya before Bharata was born to Kaikeyi. However, what if Dasaratha’s words were taken as an assurance by Asvapthi’s family? In that case, there could be obstacles to Rama ascending the throne. So Dasaratha wisely wanted Rama to be anointed while Bharata was away.