But gains are likely to be capped as concerns linger over record-high oil prices, and analysts monitor whether market conditions are as rosy as Taiwan Semiconductor Manufacturing Co (TSMC) has forecast.
"Investor confidence has recovered somewhat but we are still conservative because it is unclear whether back-to-school demand will be strong in the third quarter," said Chiang Chen-sheng, manager at MasterLink Investment Advisory.
Chiang pegged Taiwan's main TAIEX at 5,400-5,600 points this week after rising 0.9 percent last week to end at 5,420.57, its first week of gains in three.
But the index still gave up 7.2 percent in July and dipped to a closing low not seen since mid-August last year on July 26, as market players looked beyond strong quarterly profits from local tech firms and focused more on the outlook.
Despite a series of analyst downgrades on chip stocks and signs of rising inventories, the world's top contract chipmaker TSMC told investors on Thursday that third-quarter shipments would rise 4-5 percent from the second quarter.
TSMC's Taipei-listed shares ended up 4.63 percent at T$42.90 on Friday and analysts said gains could be sustained this week after it posted a record quarterly profit and raised its 2004 capital spending budget.
Smaller rival United Microelectronics Corp (UMC) also posted a near fivefold jump in quarterly profits and was upbeat on the current quarter. UMC shares were up 1.88 percent at T$21.70 on Friday.
Semiconductor-related issues make up about a third of Taiwan's total market capitalisation.
Down the production chain, battered display shares are also expected to stage a rebound after recent losses caused by concerns over weak demand from customers - makers of laptops, flat-screen monitors and televisions.
On Friday, AU Optronics Corp, the world's number-three display screen maker, finished up 0.25 percent at T$39.60 and smaller rival Chi Mei Optoelectronics Corp jumped 0.88 percent to T$45.60.
"Inventory is a concern despite a strong second quarter. What's more, we have to watch the impact from rising oil prices," said Tao Chih-wei, deputy manager of the institutional investor division at Fubon Securities.
Friday's surge in oil prices when the price of US light crude jumped to $43.15 a barrel - the highest in the New York-traded contract's 21-year history - caused worries in the markets, locally and globally.