They are betting Suga, the longtime lieutenant of outgoing prime minister Shinzo Abe who is stepping down for health reasons, will be able to secure enough votes among ruling Liberal Democratic Party (LDP) lawmakers when they hold a leadership vote on Sept. 14.
A Suga government will mean the economic, fiscal and reform policies of Abe, dubbed "Abenomics", will likely continue.
Telecom shares fell as Suga has a long-standing position of wanting to reduce mobile phone tariffs while travel-related shares soared as he said last week that he wanted to promote tourism to get the economy back on its feet.
The Nikkei bounced back and the yen regained some stability as investors expect Suga to continue policies with a focus on supporting stock prices.
"Markets are starting to price in a Suga government. He will be a successor to Abe's policies and there won't be a political vacuum," said Takashi Hiroki, chief strategist at Monex Securities.
The Nikkei <.N225> rose 1.12% to 23,139.76, wiping out all of its losses on Friday following the surprise news of Abe's resignation. The yen also steadied at 105.62 per dollar.
The three mobile phone carriers were among the worst hit on the Tokyo Stock Exchange. KDDI dropped 4.7% and NTT Docomo lost 3.4%. SoftBank, subsidiary of SoftBank Group, shed 2.7%.
Some market players also said airlines and railways gained on hopes of further measures to help revive the economy.
Suga had told Reuters last week Japan wants to avert another state of emergency and needs to consider more stimulus to revive the pandemic-hit economy.
West Japan Railway gained 3.6%, Central Japan Railway rose 3.3% and ANA Holdings added 2.6%.
"Suga's stance will be to support the economy as much as possible while trying to avoid the collapse of the medical system," said Tetsuro Ii, president of Commons Asset Management. "It's not that the stock market hugely likes him but he is well accepted."
Suga, who joins the race to take over from the country's longest-serving prime minister, will likely face off against former defence minister Shigeru Ishiba, which media polls show is the most popular choice among the public.
But the LDP is likely to use a voting method that limits the votes from rural party members, domestic media have reported, effectively blocking Ishiba's path to the prime minister's office.
Analysts say Ishiba, a rare critic of Abe within the LDP, would likely try to rein in the Bank of Japan's aggressive monetary easing, which could limit or end the central bank's exchange traded fund buying programme.
Japan's Government Pension Investment Fund, the world's largest, bought more overseas assets during Abe's administration than it did previously, including boosting purchases of Japanese equities.
These purchases could slow if the new prime minister is not committed to keeping Abe's policies in place, analysts say.
"Ishiba would try to overhaul Abenomics," said Norihiro Fujito, chief investment strategist, Mitsubishi UFJ Morgan Stanley Securities.
"An Ishiba government is what the markets fear most, but Ishiba's chances have diminished greatly. As long as someone like Suga gets the job, policy continuity will calm markets."
Fumio Kishida, a former foreign minister, and Environment Minister Shinjiro Koizumi have also been mentioned as possible successors to Abe, but analysts say neither politician has enough support to pose a serious challenge.
By Hideyuki Sano and Stanley White