Ramos moved level with Casillas as Spain's most-capped player following his 167th cap in a 4-0 rout of the Faroe Islands in Euro 2020 qualifying.
After matching Casillas in the Group F qualifier, the 33-year-old defender – who made his debut in 2005 – set a new target for himself.
"Records are there to be broken," he said.
"I hope that this momentum, enthusiasm and ambition always accompanies me and that I reach 200 games, which is the objective. You have to make it difficult."
Casillas praised Ramos after the Spain and Real Madrid skipper joined him in the history books.
"Congratulations on those 167 games! I hope there are many more," Casillas tweeted.
Ramos – winner of two European Championships in 2008 and 2012 and the 2010 World Cup – appreciated his former teammate's kind words.
"I'm flattered by Iker's praise," he said.
"I still have to overcome [his number] and I hope I can play for this country for many more years."
Braces from Rodrigo and Paco Alcacer against the Faroe Islands have put Spain firmly on track to qualify for Euro 2020.
Spain have won their opening six matches to be top and seven points clear of Sweden in Group F.
Ramos praised head coach Robert Moreno, who replaced Luis Enrique in June after the former Barcelona boss stepped down due to personal reasons before the death of his daughter last month.
"I think he is comfortable and we're delighted with him," Ramos said.
"He knows the dressing room and our way of playing well. He can help us."
Spain have won their past seven matches and will take on Norway and Sweden in October as they look to secure their place at Euro 2020.
Moreno dedicated his side's latest victory to their former coach, whose daughter was given a minute's silence prior to their match on Sunday.
"It upsets me to talk about it, but this team is his [Luis Enrique's] more than anyone's," Moreno told a news conference.
"It is a tiny thing, but we wanted to dedicate it, especially here in El Molinon."