Bashir, 68, spoke standing at a lectern for about 15 minutes in what government-owned Blue Nile TV said was a broadcast recorded earlier in the day at Sudan's embassy in Riyadh, Saudi Arabia.
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The president left hospital in the Saudi kingdom on Wednesday and was recovering there after a "successful small surgery," his second in less than four months. The operation followed a normal medical check connected to an infection in his vocal cords, official media reported.
"Israel is our enemy, our number one enemy, and we will continue calling Israel our enemy," he said in a voice which sounded normal.
The comments were his first about Israel since Khartoum accused the Jewish state of sending four radar-evading aircraft to strike the Yarmouk military factory in the heart of Khartoum at midnight on October 23.
Israel has not commented on the charge, but has long accused Sudan of channeling weapons from Iran to the Hamas-controlled Gaza Strip.
Earlier on Thursday, Bashir promised his country would respond robustly to the bombing.
"I am in perfect health, and our response to Israel will be painful," state radio quoted Bashir, 68, as saying in a brief text message sent to mobile phones.
Explosion in Khartoum arms factory (Photo: Reuters)
"After the Yarmouk incident many people were angry and asked, 'Why did this happen?', said Bashir, who smiled occasionally during his address.
To prevent another attack Sudan has two choices, he said. One is to normalize relations with Israel, which he vowed would never happen.
"The second choice is to have a technology that allows us to do an identical attack against Israel. I cannot say this is impossible. We are trying to have this technology."
After the Yarmouk compound exploded and burst into flames, speculation followed that Iranian weapons were stored or manufactured there.
Bashir came to power in a bloodless 1989 coup.
Sudanese blogs and newspapers had begun to speculate about the president's health because he has held fewer public rallies in the past few months.
Over more than two decades in power, Bashir has weathered multiple armed rebellions, years of US trade sanctions, an arrest warrant from the International Criminal Court, waves of student protests, and the secession of oil-producing South Sudan last year.
He is known for his fiery speeches and for dancing and waving his walking stick at public events.
AFP and Reuters contributed to this report
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