The 35-year-old is playing at his fifth World Cup, surpassing the four of Diego Maradona and Javier Mascherano.
With his fifth goal in Qatar, he also surpassed Gabriel Batistuta as the top Albiceleste scorer at World Cups, netting 11 times.
"It's all well and good (the records), but the important thing is to be able to achieve the group objective, which is the most beautiful thing of all," Messi added. "We're just one step away, after fighting hard, and we're going to give everything to try to make it happen this time."
Tuesday's victory prompted thousands of fans to take to the streets in Argentina to celebrate the national team's sixth World Cup final appearance.
France meet Morocco in the other semi-final later on Wednesday.