The takeover needs approval from Australia's Foreign Investment Review Board, which is likely to study it closely after regulators said they wanted to cap state-owned companies' stakes in Australia's top resource firms to 15 percent.
The fresh offer comes on the same day that China puts four employees of Ango-Australian miner Rio Tinto on trial for bribery and commercial spying, a case that has hurt relations between Australia and China.
Shell and PetroChina are now offering A$4.70 a share in cash for Arrow's Australian assets plus one share in a new listed company to be called Dart Energy, which will house its Asian exploration assets and some Australian assets, Arrow said on Monday.
The bid is pitched at a 35 percent premium to Arrow's last trade ahead of March 8, when the first offer of A$4.45 a share for the Australian assets was announced.
Arrow Energy's Managing Director Nick Davies told reporters on Monday he was "reasonably confident" that shareholders would approve the revised offer.
Disappointed investors, mostly hedge funds who piled in expecting a bigger offer, sold the shares down 3.6 percent to A$5.10.
"People probably got a bit ahead of themselves, so now we're seeing the market adjust accordingly," said Tim Schroeders, a portfolio manager at Pengana Capital, which does not own Arrow shares.
"The difficulty around it is that there probably aren't any other bidders, so Shell aren't compelled to pay the highest prices that people have seen for similar assets in the market over the past 12 months."
Analysts had said previously that an improved bid could raise the cash portion to at least A$5 a share to reflect the value of Arrow's potential reserves.
Arrow's biggest shareholder, New Hope Corp, with a 17 percent stake, had no immediate comment on the bid. New Hope Managing Director Robert Neale told Reuters he would only be able to comment after the group's board met on Monday afternoon.
Arrow has previously valued the international exploration assets at 55 cents a share. At that price, the new offer would be worth A$5.25 a share in total.
"In a nutshell, we believe this creates value now and value for the future," Chairman John Reynolds told reporters after the deal was announced.
Coal seam gas, or natural gas trapped in coal beds, has attracted global energy companies to Australia looking to export supplies to energy-hungry Asian countries, like China.
Shell is looking to use Arrow's coal seam gas to supply a planned liquefied natural gas (LNG) plant in Queensland, having lined up PetroChina to buy the gas.
Shell's LNG project will be competing against three other LNG projects in Queensland involving BG Group, ConocoPhillips, and Malaysia's Petronas.
Dart Energy will hold Arrow's international coal seam gas exploration assets in China, Indonesia, India and Vietnam as well as its stakes in BOW Energy, Apollo Gas and LNG Ltd.
Shell will continue to hold its 10 percent stake in the international assets.