"Unless we clarify who did this, trust for the Liberal Democratic Party will be shaken", Ishiba said.
When were the documents altered, and based on whose decision?
On Friday, National Tax Agency chief Nobuhisa Sagawa resigned over remarks in parliament previous year about the case.
Aso said on Monday he would not resign over the revelation.
The altered documents have fuelled suspicions of a cover-up, which could be more damaging to Abe and his finance minister, Taro Aso, than the original land sale itself, Reuters reports. Within about five minutes, Suga repeated the word "thorough investigation" five times. "It's not the case that the whole Ministry of Finance was involved".
However, opposition parties plan to raise questions about the government's involvement in the issue.
Opposition Constitutional Democratic Party of Japan leader Yukio Edano said key questions remained.
On Monday, the Finance Ministry submitted the investigation results to the Diet.
In a parliamentary hearing Monday, Finance Ministry officials confirmed that a reference to Akie Abe having recommended the land deal was deleted from a document after the scandal surfaced. However, House of Representatives member Masato Imai, a member of Kibo no To (Party of Hope), asked, "Why can you say this with certainty [while you say other issues are still being investigated]?" Outside parliament Monday, dozens of protesters demanded the Cabinet's resignation.
Abe and his government has denied the statement but their comments did little to allay people's concerns.
Abe has told parliament a year ago that he "would quit as prime minister and as a Diet member" if he or his wife Akie was found involved in the dubious land deal.More news: Trump views border wall prototypes
"Rather, this fact proves that Akie was not involved", a senior government official said.
Mr Abe has previously vowed to resign if he is found to have had links to the disputed land sale and attention is already turning to his bid to be re-elected head of the LDP - and therefore prime minister.
Forget secret meetings with foreign powers, illegal wiretapping or hotel break-ins, the scandal that dogs Japanese Prime Minister Shinzo Abe involves an elementary school.
Mr Abe and Mr Aso both apologised "deeply" over the affair amid signs the PM's popularity is suffering six months before he stands for re-election as head of the ruling LDP party.
Aso denied there had been any political pressure, but declined to disclose where the instructions came from and who was responsible. "We can't condone the attitudes of Aso and Abe, who are trying to pass the responsibility along to some officials of the Financial Bureau". Sagawa also acknowledged destroying documents.
Japanese Finance Minister Taro Aso on Tuesday reiterated that he does not intend to resign over ministry documents that were recently found to have been altered by ministry officials, saying that his job is "to investigate the cause [of the incident] and take measures to prevent a repeat". "Aso defended him too much".
The Asahi newspaper broke the news early in 2017 that Moritomo Gakuen - an educational foundation known for its nationalist leanings - had bought government land in Osaka for a fraction of the price of comparable plots.
Moreover Aso's loss would be a huge blow to Abe as he has been his deputy since 2012.
"What is important is that these things don't happen again", Aso added.
When it comes to policies, Abe also highly evaluates Aso's ability as he has played a leading role in implementing the Abenomics economic policy package together with Bank of Japan Gov. Haruhiko Kuroda.
Analysts said the slow drumbeat of the scandal would inevitably weaken Abe and his agenda.