Delta Air Lines Inc., the world’s largest carrier by traffic, said its domestic and international flights were experiencing “minimal” delays Saturday after Friday’s alleged terrorism incident aboard one of its Detroit-bound Northwest Airlines flights from Amsterdam.

Discount giant Southwest Airlines Co., which flies more passengers inside the U.S. than any other carrier, also reported only modest delays. But AMR Corp.’s American Airlines and UAL Corp.’s United Airlines, the Nos. 2 and 3 U.S. airlines by traffic, respectively, reported longer delays on international flights because of heightened security.

The U.S. Department of Homeland Security said Saturday that it immediately increased passenger-screening measures for domestic and international flights after Friday’s incident. Poor weather in parts of the U.S., particularly the Midwest, also could complicate travel on the busy holiday weekend.

Airlines flying into the U.S. tightened passenger security Saturday, and Dutch authorities said the tougher measures would stay in place indefinitely.

The National Coordinator for Counterterrorism in the Netherlands said the U.S. had asked airlines world-wide to tighten screening in an overnight request that would apply indefinitely to all U.S.-bound flights.

At London’s Heathrow airport, passengers passed through an extra layer of checks that previously had been carried out randomly. The checks can involve extra questioning and body and bag searches, though BAA, the airport operator, didn’t report any significant delays to U.S.-bound flights.

A BAA spokesman said the extra measures are the responsibility of the airlines.

Air Canada said in a news release that U.S.-bound flights were experiencing “significant delays” and urged travelers from Canada to limit their carry-on luggage to one item or even travel with no items to reduce delays.

But Susan Elliott, a spokeswoman at Atlanta-based Delta, reported “minimal” delays and cancellations on flights in the U.S. She said delays on international flights were also “minimal,” with no cancellations as of late Saturday morning.

Rain and low cloud cover in the Northeast are causing “very few delays” and snow in the Midwest is causing “some very slight delays,” she added. She declined to comment on whether heightened security was affecting travel. Delta and Northwest merged last year.

At Atlanta’s Hartfield-Jackson International Airport, Delta’s main hub and the world’s busiest airport measured by passengers, lines at security checkpoints were short and appeared to be moving briskly Saturday morning.

“This line is nothing,” said Marissa Thompson, who was walking her sisters to the security checkpoint to say goodbye to them before they departed. “I’ve been here when the line is out to the parking lot, so this line looks great.”

The winding aisles at the security gate, which help keep the lines straight as passengers wait to go through, were largely empty. Many people were able to walk straight through to have their boarding passes and identification checked by airport security officials.

Dallas-based carrier Southwest also reported few travel hitches Saturday. “Delays are scattered and not severe,” said Brad Hawkins, a airline spokesman, adding that weather conditions had improved from earlier this week.

Southwest flies only domestic flights and its operations weren’t being affected by heightened security requirements, which focused on international routes, Mr. Hawkins added.

A spokesman at Fort Worth, Texas-based American said earlier Saturday some flights to the U.S. from Europe were delayed two to three hours because of heightened security. Flights from neighboring Canada were delayed as much as three to four hours, said Tim Wagner, the spokesman.

Heavy snow in the U.S. Midwest also was affecting American flights in and out of Chicago, where travelers were experiencing delays of about two hours, Mr. Wagner added.

Chicago-based United said flights from Europe to the U.S. were being delayed between 20 minutes and 90 minutes. It also warned of delays in Chicago and Denver because of snow, but said United was planning to operate its entire schedule Saturday.

The Federal Aviation Administration’s Web site indicated late Saturday morning that departures and arrivals at Baltimore/Washington International and Teterboro airport in New Jersey, near New York City, were experiencing delays of at least 45 minutes.

Flights into John F. Kennedy International in New York, Newark International, Chicago O’Hare International and Denver International also were experiencing delays of unspecified times, according to the FAA’s Web site.

The Transportation Security Administration has been advising holiday travelers to arrive at airports two hours before departures for domestic flights and three hours before international departures.

The U.S. Department of Homeland Security had said late Friday that passengers could expect to see additional scrutiny on domestic and international flights.

A passenger on a Northwest Airlines flight en route from Amsterdam to Detroit on Friday tried to detonate an explosive device strapped to his leg and later told investigators he had affiliations with al Qaeda and was trying to blow up the plane, according to a senior U.S. official.

The incident aboard an Airbus 330-300 carrying about 280 passengers, came as the plane was approaching the airport just before noon. It landed safely after the pilots declared an emergency.

Several people flying out of Atlanta on Saturday said they felt like Friday’s incident in Detroit had no impact on their travel.

Many said the wait in security was actually shorter than they were used to — even for nonholiday travel. “It took maybe 10 minutes at most to get all the way through,” said Michael Ryan, who was flying back home to Chicago Saturday afternoon. “I wish the lines could always be that quick.”

Lines picked up slightly shortly after noon, but still didn’t appear to be causing significant wait times for passengers.